To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order vel...To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order velocity-stress wave equations for the transversely isotropic media. Comparing the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme, and the compact finite difference scheme, we analyze the approximation accuracy of these three schemes using Fourier analysis. Finally, seismic wave numerical simulation in transversely isotropic （VTI） media is performed using the three schemes. The results indicate that the compact staggered-grid finite difference scheme has the smallest truncation error, the highest accuracy, and the weakest numerical dispersion among the three schemes. In summary, the numerical modeling shows the validity of the compact staggered-grid finite difference scheme.展开更多
In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
The dynamic stress intensity factor (DSIF) and the scattering of SH wave by circle canyon and crack are studied with Green's function. In order to solve the problem, a suitable Green's function is constructed...The dynamic stress intensity factor (DSIF) and the scattering of SH wave by circle canyon and crack are studied with Green's function. In order to solve the problem, a suitable Green's function is constructed first, which is the solution of displacement fields for elastic half space with circle canyon under output plane harmonic line loading at horizontal surface. Then the integral equation for determining the unknown forces in the problem can be changed into the algebraic one and solved numerically so that crack DSIF can be determined. Last when the medium parameters are altered, the influence on the crack DSIF is discussed partially with the displacement between circle canyon and crack.展开更多
This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous ba...This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.展开更多
Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelo...Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new. In particular, our proposed method is very simple and can be applied to a lot of similar equations.展开更多
By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, ring...By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, fractal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.展开更多
The dispersion equation of the Scholte wave was reviewed using the homogeneous elastic half-space covered by a liquid layer,and the range of the Scholte wave propagation velocity was examined using the dispersion equa...The dispersion equation of the Scholte wave was reviewed using the homogeneous elastic half-space covered by a liquid layer,and the range of the Scholte wave propagation velocity was examined using the dispersion equation.The displacement expressions of the Scholte waves in liquid and solid were derived.Additionally,the mode of motion of Scholte waves in liquid and solid and their variation with depth was studied.The following results were obtained:The dispersion equation shows that the propagation velocity of the fundamental Scholte wave was greater than the P-wave in liquid and less than that of the Scholte wave in homogeneous elastic half-space.In contrast,the velocity of higher-order Scholte waves was greater than that of P waves in liquid and S-waves in solid.Only the fundamental Scholte wave has no cutoff frequency.The Scholte wave at the liquid surface moved only vertically,while the particles inside the liquid medium moved elliptically.The amplitude variation with depth in the solid medium caused the particle motion to change from a retrograde ellipse to a prograde ellipse.The above results imply the study of Scholte waves in the ocean and oceanic crust and help estimate ocean depths.展开更多
In this paper,we discussed a slab wave-guide of five layers,The core is a left-handed material,but the claddings are right-handed materials. A dispersion equation of TE modes is obtained by using Maxwell's equatio...In this paper,we discussed a slab wave-guide of five layers,The core is a left-handed material,but the claddings are right-handed materials. A dispersion equation of TE modes is obtained by using Maxwell's equations,and some new dispersion characteristics are obtained based on the equation.展开更多
New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave sol...New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.展开更多
By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact...By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.展开更多
In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method （mADM）, which is an efficient...In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method （mADM）, which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given.展开更多
By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the （1＋1）-dimensional dispersive long wave e...By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the （1＋1）-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.展开更多
For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exa...For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the （2＋l）-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.展开更多
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic co...In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.展开更多
基金supported by the National High-Tech Research and Development Program of China(Grant No.2006AA06Z202)the Open Fund of the Key Laboratory of Geophysical Exploration of CNPC(Grant No.GPKL0802)+1 种基金the Graduate Student Innovation Fund of China University of Petroleum(East China)(Grant No.S2008-1)the Program for New Century Excellent Talents in University(Grant No.NCET-07-0845)
文摘To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order velocity-stress wave equations for the transversely isotropic media. Comparing the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme, and the compact finite difference scheme, we analyze the approximation accuracy of these three schemes using Fourier analysis. Finally, seismic wave numerical simulation in transversely isotropic （VTI） media is performed using the three schemes. The results indicate that the compact staggered-grid finite difference scheme has the smallest truncation error, the highest accuracy, and the weakest numerical dispersion among the three schemes. In summary, the numerical modeling shows the validity of the compact staggered-grid finite difference scheme.
文摘In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
文摘The dynamic stress intensity factor (DSIF) and the scattering of SH wave by circle canyon and crack are studied with Green's function. In order to solve the problem, a suitable Green's function is constructed first, which is the solution of displacement fields for elastic half space with circle canyon under output plane harmonic line loading at horizontal surface. Then the integral equation for determining the unknown forces in the problem can be changed into the algebraic one and solved numerically so that crack DSIF can be determined. Last when the medium parameters are altered, the influence on the crack DSIF is discussed partially with the displacement between circle canyon and crack.
文摘This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.
文摘Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new. In particular, our proposed method is very simple and can be applied to a lot of similar equations.
文摘By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, fractal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.
基金supported by the National Natural Science Fondation of China(Nos.42174074,41674055,41704053)the Earthquake Science Spark Program of Hebei Province(No.DZ20200827053)+1 种基金Fundamental Research Funds for the Central Universities(No.ZY20215117)the Hebei Key Laboratory of Earthquake Dynamics(No.FZ212105).
文摘The dispersion equation of the Scholte wave was reviewed using the homogeneous elastic half-space covered by a liquid layer,and the range of the Scholte wave propagation velocity was examined using the dispersion equation.The displacement expressions of the Scholte waves in liquid and solid were derived.Additionally,the mode of motion of Scholte waves in liquid and solid and their variation with depth was studied.The following results were obtained:The dispersion equation shows that the propagation velocity of the fundamental Scholte wave was greater than the P-wave in liquid and less than that of the Scholte wave in homogeneous elastic half-space.In contrast,the velocity of higher-order Scholte waves was greater than that of P waves in liquid and S-waves in solid.Only the fundamental Scholte wave has no cutoff frequency.The Scholte wave at the liquid surface moved only vertically,while the particles inside the liquid medium moved elliptically.The amplitude variation with depth in the solid medium caused the particle motion to change from a retrograde ellipse to a prograde ellipse.The above results imply the study of Scholte waves in the ocean and oceanic crust and help estimate ocean depths.
基金Shanghai Leading Academic Disci- pline Project (T0102)Creative Graduate Student Foundation of Shanghai University (A.16-0107-07-001)
文摘In this paper,we discussed a slab wave-guide of five layers,The core is a left-handed material,but the claddings are right-handed materials. A dispersion equation of TE modes is obtained by using Maxwell's equations,and some new dispersion characteristics are obtained based on the equation.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx16
文摘New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.
基金Supported by the Natural Science Foundation of Education Committee of Henan Province（2003110003）
文摘By using the homogeneous balance principle（HBP）, we derive a Backtund transformation（BT） to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.
基金supported by National Natural Science Foundation of China under Grant No. 10672147
文摘In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method （mADM）, which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given.
基金The project supported by China Postdoctoral Science Foundation, Natural Science Foundation of Zhejiang Province of China under Grant No. Y604056, and Doctor Foundation of Ningbo City under Grant No. 2005A610030
文摘By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the （1＋1）-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272071, the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, and the Key Academic Discipline of Zhejiang Province under Grant No. 200412.The authors are in debt to Prof. J.F. Zhang and Dr. W.H. Huang for their helpful suggestions and fruitful discussions.
文摘For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the （2＋l）-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.
基金the National Key Basic Research Project of China under
文摘In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.
