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An analogical study of wave equations,physical quantities,conservation and reciprocity equations between electromagnetic and elastic waves
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作者 Yuchen Zang 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第11期296-304,共9页
This paper presents an analogical study between electromagnetic and elastic wave fields,with a one-to-one correspondence principle established regarding the basic wave equations,the physical quantities and the differe... This paper presents an analogical study between electromagnetic and elastic wave fields,with a one-to-one correspondence principle established regarding the basic wave equations,the physical quantities and the differential operations.Using the electromagnetic-to-elastic substitution,the analogous relations of the conservation laws of energy and momentum are investigated between these two physical fields.Moreover,the energy-based and momentum-based reciprocity theorems for an elastic wave are also derived in the time-harmonic state,which describe the interaction between two elastic wave systems from the perspectives of energy and momentum,respectively.The theoretical results obtained in this analysis can not only improve our understanding of the similarities of these two linear systems,but also find potential applications in relevant fields such as medical imaging,non-destructive evaluation,acoustic microscopy,seismology and exploratory geophysics. 展开更多
关键词 analogical study electromagnetic waves elastic waves wave equations physical quantities conservation laws reciprocity theorems
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GLOBAL CLASSICAL SOLUTIONS OF SEMILINEAR WAVE EQUATIONS ON R^(3)×T WITH CUBIC NONLINEARITIES
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作者 陶飞 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期115-128,共14页
In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the ... In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates. 展开更多
关键词 semilinear wave equation product space decay estimate energy estimate global solution
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A Hybrid Dung Beetle Optimization Algorithm with Simulated Annealing for the Numerical Modeling of Asymmetric Wave Equations
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作者 Wei Xu-ruo Bai Wen-lei +2 位作者 Liu Lu Li You-ming Wang Zhi-yang 《Applied Geophysics》 SCIE CSCD 2024年第3期513-527,618,共16页
In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two th... In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two theoretical branches of the GCM,the modified couple stress theory(M-CST)and the one-parameter second-strain-gradient theory,to form a novel asymmetric wave equation in a unified framework.Numerical modeling of the asymmetric wave equation in a unified framework accurately describes subsurface structures with vital implications for subsequent seismic wave inversion and imaging endeavors.However,employing finite-difference(FD)methods for numerical modeling may introduce numerical dispersion,adversely affecting the accuracy of numerical modeling.The design of an optimal FD operator is crucial for enhancing the accuracy of numerical modeling and emphasizing the scale effects.Therefore,this study devises a hybrid scheme called the dung beetle optimization(DBO)algorithm with a simulated annealing(SA)algorithm,denoted as the SA-based hybrid DBO(SDBO)algorithm.An FD operator optimization method under the SDBO algorithm was developed and applied to the numerical modeling of asymmetric wave equations in a unified framework.Integrating the DBO and SA algorithms mitigates the risk of convergence to a local extreme.The numerical dispersion outcomes underscore that the proposed SDBO algorithm yields FD operators with precision errors constrained to 0.5‱while encompassing a broader spectrum coverage.This result confirms the efficacy of the SDBO algorithm.Ultimately,the numerical modeling results demonstrate that the new FD method based on the SDBO algorithm effectively suppresses numerical dispersion and enhances the accuracy of elastic wave numerical modeling,thereby accentuating scale effects.This result is significant for extracting wavefield perturbations induced by complex microstructures in the medium and the analysis of scale effects. 展开更多
关键词 FINITE-DIFFERENCE Asymmetric wave equation Numerical modeling DBO algorithm SA algorithm
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Target-oriented Q-compensated reverse-time migration by using optimized pure-mode wave equation in anisotropic media 被引量:1
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作者 Shi-Gang Xu Qian-Zong Bao Zhi-Ming Ren 《Petroleum Science》 SCIE EI CAS CSCD 2023年第2期866-878,共13页
Research on seismic anisotropy and attenuation plays a significant role in exploration geophysics. To enhance the imaging quality for complicated structures, we develop several effective improvements for anisotropic a... Research on seismic anisotropy and attenuation plays a significant role in exploration geophysics. To enhance the imaging quality for complicated structures, we develop several effective improvements for anisotropic attenuation effects in reverse-time migration (Q-RTM) on surface and vertical seismic profiling (VSP) acquisition geometries. First, to suppress pseudo-shear wave artifact and numerical instability of the commonly used anisotropic pseudo-acoustic wave equations, an optimized pure P-wave dispersion relation is derived and the corresponding pure-mode wave equation is solved by combining the finite-difference and Possion methods. Second, a simplified anisotropic pure-mode visco-acoustic wave equation (PVAWE) based on standard linear solid model is established. Third, a time-dispersion correlation strategy is applied to improve the modeling accuracy. Fourth, we extend a target-oriented scheme to anisotropic attenuated modeling and imaging. Instead of the conventional wavefield modeling and RTM, the proposed approach can extract available wavefield information near the target regions and produce high imaging resolution for target structures. Last, both anisotropic surface and VSP Q-RTMs are executed by combining optimized PVAWE, time-dispersion correlation and target-oriented algorithm. Modeling examples demonstrate the advantages of our schemes. Moreover, our modified Q-compensated imaging workflow can be regarded as a supplement to the classical anisotropic RTM. 展开更多
关键词 ANISOTROPY ATTENUATION Reverse-time migration wave equation Optimized algorithm Target-oriented
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Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations 被引量:1
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作者 刘希忠 李界通 俞军 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第11期313-319,共7页
Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of t... Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated. 展开更多
关键词 (3+1)-dimensional shallow water wave equation residual symmetry consistent Riccati expansion
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Preserved amplitude migration based on the one way wave equation in the angle domain 被引量:5
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作者 叶月明 李振春 +2 位作者 徐秀刚 朱绪峰 仝兆岐 《Applied Geophysics》 SCIE CSCD 2009年第1期50-58,103,共10页
Traditional pre-stack depth migration can only provide subsurface structural information. However, simple structure information is insufficient for petroleum exploration which also needs amplitude information proporti... Traditional pre-stack depth migration can only provide subsurface structural information. However, simple structure information is insufficient for petroleum exploration which also needs amplitude information proportional to reflection coefficients. In recent years, pre-stack depth migration algorithms which preserve amplitudes and based on the one- way wave equation have been developed. Using the method in the shot domain requires a deconvolution imaging condition which produces some instability in areas with complicated structure and dramatic lateral variation in velocity. Depth migration with preserved amplitude based on the angle domain can overcome the instability of the one-way wave migration imaging condition with preserved amplitude. It can also offer provide velocity analysis in the angle domain of common imaging point gathers. In this paper, based on the foundation of the one-way wave continuation operator with preserved amplitude, we realized the preserved amplitude prestack depth migration in the angle domain. Models and real data validate the accuracy of the method. 展开更多
关键词 Preserved amplitude prestack depth migration angle domain one way wave equation imaging conditions
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Three-dimensional acoustic wave equation modeling based on the optimal finite-difference scheme 被引量:4
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作者 蔡晓慧 刘洋 +4 位作者 任志明 王建民 陈志德 陈可洋 王成 《Applied Geophysics》 SCIE CSCD 2015年第3期409-420,469,共13页
Generally, FD coefficients can be obtained by using Taylor series expansion (TE) or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a... Generally, FD coefficients can be obtained by using Taylor series expansion (TE) or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares (LS) can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional (2D) forward modeling to three-dimensional (3D) and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods. 展开更多
关键词 3D acoustic wave equation optimal finite-difference forward modeling reversetime migration
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Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations 被引量:3
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作者 赵建国 史瑞其 《Applied Geophysics》 SCIE CSCD 2013年第3期323-336,359,共15页
The perfectly matched layer (PML) is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-eleme... The perfectly matched layer (PML) is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media. 展开更多
关键词 Absorbing boundary condition elastic wave equation perfectly matched layer finite-element modeling
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On the Asymptotic Property of Solutions to Some Nonlinear Dissipative Wave Equations 被引量:1
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作者 梁保松 叶耀军 李慧平 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第4期83-86,共4页
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.
关键词 nonlinear wave equation asymtotic property global solution
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The Global Uniqueness of Solutions for a Class of Inverse Problem in 1-D Wave Equations of Hyperbolic Type 被引量:1
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作者 叶留青 司清亮 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第3期107-110,共4页
This paper has given the global uniquene ss theory of solutions for a class of inverse problem in 1_D Wave equation of hype rbolic type.
关键词 D wave equations of hyperbolic inverse proble m global uniqueness
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On the Blowing-up Behaviours for Nonlirear Wave Equations 被引量:5
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作者 张健 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第1期11-17,共7页
This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite tim... This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite time to the mixed problems with respect to Neumann boundary and Dirichlet boundary for various nonlinear conditions and initial value conditions which usually meet. 展开更多
关键词 nonlinear wave equation BLOW-UP
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Weak solution for a fourth-order nonlinear wave equation
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作者 陈才生 任磊 《Journal of Southeast University(English Edition)》 EI CAS 2005年第3期369-374,共6页
The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt+αΔ2 u-bΔut-βΔu+ut|ut|^r+g(u)=0 in Ω×(0,∞) are studied w... The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt+αΔ2 u-bΔut-βΔu+ut|ut|^r+g(u)=0 in Ω×(0,∞) are studied with the boundary condition u=(u)/(υ)=0 onΩ and the initial condition u(x,0)=u0(x),ut(x,0)=u1(x,0) in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method. 展开更多
关键词 nonlinear wave equation UNIQUENESS energy decay estimate blow up
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P-and S-wavefield simulations using both the firstand second-order separated wave equations through a high-order staggered grid finite-difference method
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作者 Chao-ying Bai Xin Wang Cai-xia Wang 《Earthquake Science》 2013年第2期83-98,共16页
In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this... In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations: the first-order (velocity-stress) and the second- order (displacement-stress) separate elastic wave equa- tions, with the first-order (velocity-stress) and the second- order (displacement-stress) full (or mixed) elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements. 展开更多
关键词 Finite-difference method Staggeredgrid First-order separate elastic wave equation Second-order separate elastic wave equation Multiple arrival tracking
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Linear superposition solutions to nonlinear wave equations
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作者 刘煜 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第11期39-44,共6页
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this articl... The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed. 展开更多
关键词 linear superposition solution nonlinear wave equation generalized KdV equation Oliverwater wave equation
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Pure quasi-P wave equation and numerical solution in 3D TTI media 被引量:3
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作者 张建敏 何兵寿 唐怀谷 《Applied Geophysics》 SCIE CSCD 2017年第1期125-132,191,共9页
Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis (VTI media), a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis (TTI me... Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis (VTI media), a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis (TTI media). This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ε. The finite difference method is used to solve the equation. In addition, a perfectly matched layer (PML) absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium. 展开更多
关键词 TTI media the pure quasi-P wave equation high-order finite PML boundary conditions BP model
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3D elastic wave equation forward modeling based on the precise integration method 被引量:1
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作者 段玉婷 胡天跃 +1 位作者 姚逢昌 张研 《Applied Geophysics》 SCIE CSCD 2013年第1期71-78,118,119,共10页
The Finite Difference (FD) method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data... The Finite Difference (FD) method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data. However, because of its discretization, the FD method is only stable under certain conditions. The Arbitrary Difference Precise Integration (ADPI) method is based on the FD method and adopts an integration scheme in the time domain and an arbitrary difference scheme in the space domain. Therefore, the ADPI method is a semi-analytical method. In this paper, we deduce the formula for the ADPI method based on the 3D elastic equation and improve its stability. In forward modeling cases, the ADPI method was implemented in 2D and 3D elastic wave equation forward modeling. Results show that the travel time of the reflected seismic wave is accurate. Compared with the acoustic wave field, the elastic wave field contains more wave types, including PS- and PP- reflected waves, transmitted waves, and diffracted waves, which is important to interpretation of seismic data. The method can be easily applied to elastic wave equation numerical simulations for eoloical models. 展开更多
关键词 Arbitrary difference precise integration method elastic waves wave equation seismic numerical simulation
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A New Approach to Solve Nonlinear Wave Equations 被引量:15
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作者 FUZun-Tao LIUShi-Kuo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2003年第1期27-30,共4页
From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that ... From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions. 展开更多
关键词 sine-Gordon equation Jacobi elliptic function nonlinear wave equation periodic wave solution solitary wave solution
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Invariant Sets and Exact Solutions to Higher-Dimensional Wave Equations 被引量:11
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作者 QU Gai-Zhu ZHANG Shun-Li ZHU Chun-Rong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第5期1119-1124,共6页
The invariant sets and exact solutions of the (1 + 2)-dimensional wave equations are discussed. It is shown that there exist a class of solutions to the equations which belong to the invariant set E0 = {u : ux = ... The invariant sets and exact solutions of the (1 + 2)-dimensional wave equations are discussed. It is shown that there exist a class of solutions to the equations which belong to the invariant set E0 = {u : ux = vxF(u),uy = vyF(u) }. This approach is also developed to solve (1 + N)-dimensional wave equations. 展开更多
关键词 wave equation invariant set exact solution
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Exact travelling wave solutions for (1+ 1)-dimensional dispersive long wave equation 被引量:15
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作者 刘成仕 《Chinese Physics B》 SCIE EI CAS CSCD 2005年第9期1710-1715,共6页
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral fo... A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems. 展开更多
关键词 complete discrimination system for polynomial (1+1)-dimensional dispersive long wave equation travelling wave solution
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Extended Group Foliation Method and Functional Separation of Variables to Nonlinear Wave Equations 被引量:9
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作者 QU Chang-Zheng ZHANG Shun-Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第4X期577-582,共6页
Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to n... Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach. 展开更多
关键词 symmetry group group foliation method nonlinear wave equation functional separation of variables
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