The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattic...The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .展开更多
We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the Geometric Theory of Diffraction(GTD)to simulate the high frequency linear waves diffracted by a half plane.We first ...We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the Geometric Theory of Diffraction(GTD)to simulate the high frequency linear waves diffracted by a half plane.We first introduce a condition,based on the GTD theory,at the vertex of the half plane to account for the diffractions,and then build in this condition as well as the reflection boundary condition into the numerical flux of the geometrical optics Liouville equation.Numerical experiments are used to verify the validity and accuracy of this new Eulerian numerical method which is able to capture the moments of high frequency and diffracted waves without fully resolving the high frequency numerically.展开更多
This paper addresses the application of the continuum mechanics-based multiplicative decomposition for thermohyperelastic materials by Lu and Pister to Reissner’s structural mechanics-based,geometrically exact theory...This paper addresses the application of the continuum mechanics-based multiplicative decomposition for thermohyperelastic materials by Lu and Pister to Reissner’s structural mechanics-based,geometrically exact theory for finite strain plane deformations of beams,which represents a geometrically consistent non-linear extension of the linear shear-deformable Timoshenko beam theory.First,the Lu-Pister multiplicative decomposition of the displacement gradient tensor is reviewed in a three-dimensional setting,and the importance of its main consequence is emphasized,i.e.,the fact that isothermal experiments conducted over a range of constant reference temperatures are sufficient to identify constitutive material parameters in the stress-strain relations.We address various isothermal stress-strain relations for isotropic hyperelastic materials and their extensions to thermoelasticity.In particular,a model belonging to what is referred to as Simo-Pister class of material laws is used as an example to demonstrate the proposed procedure to extend isothermal stress-strain relations for isotropic hyperelastic materials to thermoelasticity.A certain drawback of Reissner’s structural-mechanics based theory in its original form is that constitutive relations are to be stipulated at the one-dimensional level,between stress resultants and generalized strains,so that the standardized small-scale material testing at the stress-strain level is not at disposal.In order to overcome this,we use a stress-strain based extension of the Reissner theory proposed by Gerstmayr and Irschik for the isothermal case,which we utilize here in the framework of the considered thermoelastic extension of the Simo-Pister stressstrain law.Consistent with the latter extension,we derive non-linear thermo-hyperelastic constitutive relations between stress-resultants and general strains.Special emphasis is given to linearizations and their consequences.A numerical example demonstrates the efficacy of the structural-mechanics approach in large-deformation problems.展开更多
The geometries, stabilities, and electronic properties of FSin (n=1~12) clusters are systematically investigated by using first-principles calculations based on the hybrid density-functional theory at the B3LYP/6-3...The geometries, stabilities, and electronic properties of FSin (n=1~12) clusters are systematically investigated by using first-principles calculations based on the hybrid density-functional theory at the B3LYP/6-311G level. The geometries are found to undergo a structural change from two-dimensional to three-dimensional structure when the cluster size n equals 3. On the basis of the obtained lowest-energy geometries, the size dependencies of cluster properties, such as averaged binding energy, fragmentation energy, second-order energy difference, HOMO–LUMO (highest occupied molecular orbital–lowest unoccupied molecular orbital) gap and chemical hardness, are discussed. In addition, natural population analysis indicates that the F atom in the most stable FSin cluster is recorded as being negative and the charges always transfer from Si atoms to the F atom in the FSin clusters.展开更多
The noise robustness and parameter estimation performance of the classical three-dimensional estimating signal parameter via rotational invariance techniques(3D-ESPRIT)algorithm are poor when the parameters of the geo...The noise robustness and parameter estimation performance of the classical three-dimensional estimating signal parameter via rotational invariance techniques(3D-ESPRIT)algorithm are poor when the parameters of the geometric theory of the diffraction(GTD)model are estimated at low signal-to-noise ratio(SNR).To solve this problem,a modified 3D-ESPRIT algorithm is proposed.The modified algorithm improves the parameter estimation accuracy by proposing a novel spatial smoothing technique.Firstly,we make cross-correlation of the auto-correlation matrices;then by averaging the cross-correlation matrices of the forward and backward spatial smoothing,we can obtain a novel equivalent spatial smoothing matrix.The formula of the modified algorithm is derived and the performance of this improved method is also analyzed.Then we compare root-meansquare-errors(RMSEs)of different parameters and the locating accuracy obtained by different algorithms.Furthermore,radar cross section(RCS)of radar targets is extrapolated.Simulation results verify the effectiveness and superiority of the modified 3DESPRIT algorithm.展开更多
Understanding the physical features of the diffracted sound field on the surface of an axisymmetric body is important for predicting the self-noise of a sonar mounted on an underwater platform. The diffracted sound fi...Understanding the physical features of the diffracted sound field on the surface of an axisymmetric body is important for predicting the self-noise of a sonar mounted on an underwater platform. The diffracted sound field from the transition region of an axisymmetric body was calculated by the geometrical theory of diffraction. The diffraction ray between the source point and the receiving point on the surface of an axisymmetric body was calculated by using the dynamic programming method. Based on the diffracted sound field, a simulation scheme for the noise correlation of the conformal array was presented. It was shown that the normalized pressure of the diffracted sound field from the transition region reduced with the increases of the frequency and the curvature of the ray. The flow noises of two models were compared and a rather optimum fore-body geometric shape was given. Furthermore, it was shown that the correlation of the flow noise in the low frequencies was stronger than that in the high frequencies. And the flow noise received by the acoustic array on the curved surface had a stronger correlation than that on the head plane at the designed center frequency, which is important for sonar system design.展开更多
The scattering characteristics of electromagnetic waves from buildings are presented. The uniform geometric theory of diffraction (UTD) is employed to approximate the near field-far field distribution. The numerical r...The scattering characteristics of electromagnetic waves from buildings are presented. The uniform geometric theory of diffraction (UTD) is employed to approximate the near field-far field distribution. The numerical results presented demonstrate that the UTD solution can be conveniently and efficiently applied to many practical problems. As such results are of importance to the mobile communication field.展开更多
Some techniques in the Geometric Measure Theory are used to study the hypersurfaces in Euclidean spaces and some fundamental properties with this subject are discussed in this article.
Localized deformation and instability is the focal point of research in mechanics. The most typical problem is the plastic analysis of cylindrical bar neckingand shear band under uniaxial tension. Traditional elasto-...Localized deformation and instability is the focal point of research in mechanics. The most typical problem is the plastic analysis of cylindrical bar neckingand shear band under uniaxial tension. Traditional elasto-plastic mechanics of infinitesimal deformation can not solve this problem successfully. In this paper, on the basis of S(strain) -R(rotation) decomposition theorem, the authors obtain the localstrain distribution and progressive state of axial symmetric finite deformation of cylindrical bar under uniaxial tension adopting nonlinear gauge approximate method and computer modelling technique.展开更多
In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic me...In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic method. The Cauchy-Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy-Pompeiu formula.展开更多
Time-delay effects on synchronization features of delay-coupled slow-fast van der Pol systems are investigated in the present paper. The synchronization mechanism of “slow-manifold adjustment” is firstly described o...Time-delay effects on synchronization features of delay-coupled slow-fast van der Pol systems are investigated in the present paper. The synchronization mechanism of “slow-manifold adjustment” is firstly described on the basis of geometric singular perturbation theory. Then, the impact of time delay on the structure of the slow manifold of synchronized system is obtained by using the method of stability switch, and thus, time-delay effects on synchronization features are stated. It is shown the time delay cannot qualitatively affect the synchronization mechanism, however, it can result in the drift of the optimal coupling strength.展开更多
Jumping sun dogs are rapid light flashes changing over clouds, with some of them located close to the places of halo formation in thunder storms clouds. This paper presents an outline of some aspects that are required...Jumping sun dogs are rapid light flashes changing over clouds, with some of them located close to the places of halo formation in thunder storms clouds. This paper presents an outline of some aspects that are required for understanding the jumping sun dogs, using some experiments with light scattering in complex fluids. In our analogy, we have observed the jumping laser dogs, in which the ice crystals are replaced by needlelike structures of ferrofluid, the electric field in the atmosphere is represented by an external magnetic field, and the laser beam scattered by the ferrofluid structure has the same role of the sun as the source of light scattered by the ice crystals subjected to changing electric fields in thunderstorm clouds.展开更多
A novel method to extract conic blending feature in reverse engineering is presented. Different from the methods to recover constant and variable radius blends from unorganized points, it contains not only novel segme...A novel method to extract conic blending feature in reverse engineering is presented. Different from the methods to recover constant and variable radius blends from unorganized points, it contains not only novel segmentation and feature recognition techniques, but also bias corrected technique to capture more reliable distribution of feature parameters along the spine curve. The segmentation depending on point classification separates the points in the conic blend region from the input point cloud. The available feature parameters of the cross-sectional curves are extracted with the processes of slicing point clouds with planes, conic curve fitting, and parameters estimation and compensation, The extracted parameters and its distribution laws are refined according to statistic theory such as regression analysis and hypothesis test. The proposed method can accurately capture the original design intentions and conveniently guide the reverse modeling process. Application examples are presented to verify the high precision and stability of the proposed method.展开更多
The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as...The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.展开更多
This paper proposes a new neural algorithm to perform the segmentation of an observed scene into regions corresponding to different moving objects byanalyzing a time-varying images sequence. The method consists of a c...This paper proposes a new neural algorithm to perform the segmentation of an observed scene into regions corresponding to different moving objects byanalyzing a time-varying images sequence. The method consists of a classificationstep, where the motion of small patches is characterized through an optimizationapproach, and a segmentation step merging neighboring patches characterized bythe same motion. Classification of motion is performed without optical flow computation, but considering only the spatial and temporal image gradients into anappropriate energy function minimized with a Hopfield-like neural network givingas output directly the 3D motion parameter estimates. Network convergence is accelerated by integrating the quantitative estimation of motion parameters with aqualitative estimate of dominant motion using the geometric theory of differentialequations.展开更多
The truncation equation for the derivative nonlinear Schrodinger equation has been dis- cussed in this paper. The existence of a special heteroclinic orbit has been found by using geometrical singular perturbation the...The truncation equation for the derivative nonlinear Schrodinger equation has been dis- cussed in this paper. The existence of a special heteroclinic orbit has been found by using geometrical singular perturbation theory together with Melnikov's technique.展开更多
Let K be a compact group.For a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*)...Let K be a compact group.For a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*).To prove such a result,we take two di erent approaches:(i)use the complex geometry properties of the symplectic implosion construction;(ii)investigate the variation of geometric invariant theory(GIT)quotients.展开更多
This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|^(2)-2uv-τu(|u|^(2))x=0 vtt+vxx-β(|u|^(x))xx=0.We first establish the existence of s...This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|^(2)-2uv-τu(|u|^(2))x=0 vtt+vxx-β(|u|^(x))xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.展开更多
文摘The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .
文摘We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the Geometric Theory of Diffraction(GTD)to simulate the high frequency linear waves diffracted by a half plane.We first introduce a condition,based on the GTD theory,at the vertex of the half plane to account for the diffractions,and then build in this condition as well as the reflection boundary condition into the numerical flux of the geometrical optics Liouville equation.Numerical experiments are used to verify the validity and accuracy of this new Eulerian numerical method which is able to capture the moments of high frequency and diffracted waves without fully resolving the high frequency numerically.
基金The authors acknowledge the support by the Linz Center of Mechatronics(LCM)in the framework of the Austrian COMET-K2 program。
文摘This paper addresses the application of the continuum mechanics-based multiplicative decomposition for thermohyperelastic materials by Lu and Pister to Reissner’s structural mechanics-based,geometrically exact theory for finite strain plane deformations of beams,which represents a geometrically consistent non-linear extension of the linear shear-deformable Timoshenko beam theory.First,the Lu-Pister multiplicative decomposition of the displacement gradient tensor is reviewed in a three-dimensional setting,and the importance of its main consequence is emphasized,i.e.,the fact that isothermal experiments conducted over a range of constant reference temperatures are sufficient to identify constitutive material parameters in the stress-strain relations.We address various isothermal stress-strain relations for isotropic hyperelastic materials and their extensions to thermoelasticity.In particular,a model belonging to what is referred to as Simo-Pister class of material laws is used as an example to demonstrate the proposed procedure to extend isothermal stress-strain relations for isotropic hyperelastic materials to thermoelasticity.A certain drawback of Reissner’s structural-mechanics based theory in its original form is that constitutive relations are to be stipulated at the one-dimensional level,between stress resultants and generalized strains,so that the standardized small-scale material testing at the stress-strain level is not at disposal.In order to overcome this,we use a stress-strain based extension of the Reissner theory proposed by Gerstmayr and Irschik for the isothermal case,which we utilize here in the framework of the considered thermoelastic extension of the Simo-Pister stressstrain law.Consistent with the latter extension,we derive non-linear thermo-hyperelastic constitutive relations between stress-resultants and general strains.Special emphasis is given to linearizations and their consequences.A numerical example demonstrates the efficacy of the structural-mechanics approach in large-deformation problems.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11304167 and 51374132)the Postdoctoral Science Foundation of China(Grant No.20110491317)+1 种基金the Young Core Instructor Foundation of Henan Province,China(Grant No.2012GGJS-152)the Natural Science Foundation of Henan Province,China(Grant Nos.132300410209 and 132300410290)
文摘The geometries, stabilities, and electronic properties of FSin (n=1~12) clusters are systematically investigated by using first-principles calculations based on the hybrid density-functional theory at the B3LYP/6-311G level. The geometries are found to undergo a structural change from two-dimensional to three-dimensional structure when the cluster size n equals 3. On the basis of the obtained lowest-energy geometries, the size dependencies of cluster properties, such as averaged binding energy, fragmentation energy, second-order energy difference, HOMO–LUMO (highest occupied molecular orbital–lowest unoccupied molecular orbital) gap and chemical hardness, are discussed. In addition, natural population analysis indicates that the F atom in the most stable FSin cluster is recorded as being negative and the charges always transfer from Si atoms to the F atom in the FSin clusters.
基金This work was supported by the National Natural Science Foundation of China(61372033).
文摘The noise robustness and parameter estimation performance of the classical three-dimensional estimating signal parameter via rotational invariance techniques(3D-ESPRIT)algorithm are poor when the parameters of the geometric theory of the diffraction(GTD)model are estimated at low signal-to-noise ratio(SNR).To solve this problem,a modified 3D-ESPRIT algorithm is proposed.The modified algorithm improves the parameter estimation accuracy by proposing a novel spatial smoothing technique.Firstly,we make cross-correlation of the auto-correlation matrices;then by averaging the cross-correlation matrices of the forward and backward spatial smoothing,we can obtain a novel equivalent spatial smoothing matrix.The formula of the modified algorithm is derived and the performance of this improved method is also analyzed.Then we compare root-meansquare-errors(RMSEs)of different parameters and the locating accuracy obtained by different algorithms.Furthermore,radar cross section(RCS)of radar targets is extrapolated.Simulation results verify the effectiveness and superiority of the modified 3DESPRIT algorithm.
基金Project supported by the National Natural Science Foundational of China (Grant No.10774119)the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No.NCET-08-0455)+2 种基金the Natural Science Foundation of Shaanxi Province of China (Grant No.SJ08F07)the Foundation of National Laboratory of Acoustics of Chinathe Foundation for Fundamental Research of Northwestern Polytechnical University of China (Grant No.2007004)
文摘Understanding the physical features of the diffracted sound field on the surface of an axisymmetric body is important for predicting the self-noise of a sonar mounted on an underwater platform. The diffracted sound field from the transition region of an axisymmetric body was calculated by the geometrical theory of diffraction. The diffraction ray between the source point and the receiving point on the surface of an axisymmetric body was calculated by using the dynamic programming method. Based on the diffracted sound field, a simulation scheme for the noise correlation of the conformal array was presented. It was shown that the normalized pressure of the diffracted sound field from the transition region reduced with the increases of the frequency and the curvature of the ray. The flow noises of two models were compared and a rather optimum fore-body geometric shape was given. Furthermore, it was shown that the correlation of the flow noise in the low frequencies was stronger than that in the high frequencies. And the flow noise received by the acoustic array on the curved surface had a stronger correlation than that on the head plane at the designed center frequency, which is important for sonar system design.
文摘The scattering characteristics of electromagnetic waves from buildings are presented. The uniform geometric theory of diffraction (UTD) is employed to approximate the near field-far field distribution. The numerical results presented demonstrate that the UTD solution can be conveniently and efficiently applied to many practical problems. As such results are of importance to the mobile communication field.
基金Supported by a Grant-in-Aid for scicntific Research from Nanjing University of Science and Technology (AB96137) partly by NNSP(10471063)
文摘Some techniques in the Geometric Measure Theory are used to study the hypersurfaces in Euclidean spaces and some fundamental properties with this subject are discussed in this article.
文摘Localized deformation and instability is the focal point of research in mechanics. The most typical problem is the plastic analysis of cylindrical bar neckingand shear band under uniaxial tension. Traditional elasto-plastic mechanics of infinitesimal deformation can not solve this problem successfully. In this paper, on the basis of S(strain) -R(rotation) decomposition theorem, the authors obtain the localstrain distribution and progressive state of axial symmetric finite deformation of cylindrical bar under uniaxial tension adopting nonlinear gauge approximate method and computer modelling technique.
基金supported by NNSF of China(11171260)RFDP of Higher Education of China(20100141110054)
文摘In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic method. The Cauchy-Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy-Pompeiu formula.
文摘Time-delay effects on synchronization features of delay-coupled slow-fast van der Pol systems are investigated in the present paper. The synchronization mechanism of “slow-manifold adjustment” is firstly described on the basis of geometric singular perturbation theory. Then, the impact of time delay on the structure of the slow manifold of synchronized system is obtained by using the method of stability switch, and thus, time-delay effects on synchronization features are stated. It is shown the time delay cannot qualitatively affect the synchronization mechanism, however, it can result in the drift of the optimal coupling strength.
文摘Jumping sun dogs are rapid light flashes changing over clouds, with some of them located close to the places of halo formation in thunder storms clouds. This paper presents an outline of some aspects that are required for understanding the jumping sun dogs, using some experiments with light scattering in complex fluids. In our analogy, we have observed the jumping laser dogs, in which the ice crystals are replaced by needlelike structures of ferrofluid, the electric field in the atmosphere is represented by an external magnetic field, and the laser beam scattered by the ferrofluid structure has the same role of the sun as the source of light scattered by the ice crystals subjected to changing electric fields in thunderstorm clouds.
基金This project is supported by General Electric Company and National Advanced Technology Project of China(No.863-511-942-018).
文摘A novel method to extract conic blending feature in reverse engineering is presented. Different from the methods to recover constant and variable radius blends from unorganized points, it contains not only novel segmentation and feature recognition techniques, but also bias corrected technique to capture more reliable distribution of feature parameters along the spine curve. The segmentation depending on point classification separates the points in the conic blend region from the input point cloud. The available feature parameters of the cross-sectional curves are extracted with the processes of slicing point clouds with planes, conic curve fitting, and parameters estimation and compensation, The extracted parameters and its distribution laws are refined according to statistic theory such as regression analysis and hypothesis test. The proposed method can accurately capture the original design intentions and conveniently guide the reverse modeling process. Application examples are presented to verify the high precision and stability of the proposed method.
文摘The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.
文摘This paper proposes a new neural algorithm to perform the segmentation of an observed scene into regions corresponding to different moving objects byanalyzing a time-varying images sequence. The method consists of a classificationstep, where the motion of small patches is characterized through an optimizationapproach, and a segmentation step merging neighboring patches characterized bythe same motion. Classification of motion is performed without optical flow computation, but considering only the spatial and temporal image gradients into anappropriate energy function minimized with a Hopfield-like neural network givingas output directly the 3D motion parameter estimates. Network convergence is accelerated by integrating the quantitative estimation of motion parameters with aqualitative estimate of dominant motion using the geometric theory of differentialequations.
文摘The truncation equation for the derivative nonlinear Schrodinger equation has been dis- cussed in this paper. The existence of a special heteroclinic orbit has been found by using geometrical singular perturbation theory together with Melnikov's technique.
基金supported by China Postdoctoral Science Foundation(Grant No.BX201700008).
文摘Let K be a compact group.For a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*).To prove such a result,we take two di erent approaches:(i)use the complex geometry properties of the symplectic implosion construction;(ii)investigate the variation of geometric invariant theory(GIT)quotients.
基金Supported by NSFC(Grant Nos.12071065 and 11871140)the National Key Research and Development Program of China(Grant No.2020YFA0713602)。
文摘This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|^(2)-2uv-τu(|u|^(2))x=0 vtt+vxx-β(|u|^(x))xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.