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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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Collisions Between Lumps/Rogue Waves and Solitons for A(3+1)-Dimensional Generalized Variable-Coefficient Shallow Water Wave Equation
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作者 WU Xiao-yu DU Zhong 《China Ocean Engineering》 SCIE EI CSCD 2022年第5期808-813,共6页
In this paper,we investigate a(3+1)-dimensional generalized variable-coefficient shallow water wave equation,which can be used to describe the flow below a pressure surface in oceanography and atmospheric science.Empl... In this paper,we investigate a(3+1)-dimensional generalized variable-coefficient shallow water wave equation,which can be used to describe the flow below a pressure surface in oceanography and atmospheric science.Employing the Kadomtsev−Petviashvili hierarchy reduction,we obtain the semi-rational solutions which describe the lumps and rogue waves interacting with the kink solitons.We find that the lump appears from one kink soliton and fuses into the other on the x−y and x−t planes.However,on the x−z plane,the localized waves in the middle of the parallel kink solitons are in two forms:lumps and line rogue waves.The effects of the variable coefficients on the two forms are discussed.The dispersion coefficient influences the speed of solitons,while the background coefficient influences the background’s height. 展开更多
关键词 variable-coefficient shallow water wave equation lumps linear rogue waves Kadomtsev-Petviashvili hierarchy reduction
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Some New Nonlinear Wave Solutions for a Higher-Dimensional Shallow Water Wave Equation
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作者 Longmin Dong Zhu Guo Yinghui He 《Journal of Applied Mathematics and Physics》 2020年第9期1845-1860,共16页
In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries.... In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries. Moreover, with the extended <em>F</em>-expansion method, we obtain several new nonlinear wave solutions involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function and trigonometric function. 展开更多
关键词 shallow Water wave equations Nonlinear wave Solution Lie Symmetry Analysis Extended F-Expansion Method
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Direct Approach to Construct the Periodic Wave Solutions for Two Nonlinear Evolution Equations 被引量:2
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作者 CAI Ke-Jie TIAN Bo +1 位作者 ZHANG Huan MENG Xiang-Hua 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第9期473-478,共6页
With symbolic computation, the Hirota method and Riemann theta function are employed to directly construct the periodic wave solutions for the Hirota-Satsuma equation for shallow water waves and Boiti-Leon-Manna- Pemp... With symbolic computation, the Hirota method and Riemann theta function are employed to directly construct the periodic wave solutions for the Hirota-Satsuma equation for shallow water waves and Boiti-Leon-Manna- Pempinelli equation. Then, the corresponding figures of the periodic wave solutions are given. Fhrthermore, it is shown that the known soliton solutions can be reduced from the periodic wave solutions. 展开更多
关键词 periodic wave solutions Hirota-Satsuma equation for shallow water waves Boiti-Leon-Manna-Pempinelli equation Hirota method Riemann theta function
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Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility 被引量:8
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作者 Mostafa F.El-Sabbagh Ahmad T.Ali 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第10期611-616,共6页
The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the... The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples i11ustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries. 展开更多
关键词 nonclassical symmetriesm compatibility (2+ 1)-dimensional shallow water wave Boussinesq equa-tions and the dispersive wave equations in shallow water
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Dispersive soliton solutions for shallow water wave system and modified Benjamin-Bona-Mahony equations via applications of mathematical methods 被引量:3
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作者 Asghar Ali Aly R.Seadawy 《Journal of Ocean Engineering and Science》 SCIE 2021年第1期85-98,共14页
We have utilized three novel methods,called generalized direct algebraic,modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations an... We have utilized three novel methods,called generalized direct algebraic,modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations and modified Benjamin-Bona-Mahony equation.After substituting particular values of the parameters,different solitary wave solutions are derived from the exact traveling wave solutions.It is shown that these employed methods are more powerful tools for nonlinear wave equations. 展开更多
关键词 System of shallow water wave equations Modified Benjamin-Bona-Mahony equation Generalized direct algebraic method Improved simple equation method Modified F-expansion method Traveling wave solutions Solitary wave solutions
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Darboux Transformation and Soliton Solutions for the (2+1)-Dimensional Generalization of Shallow Water Wave Equation with Symbolic Computation
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作者 闻小永 孟祥花 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第8期194-200,共7页
In this paper, the (2+l)-dimensional generalization of shallow water wave equation, which may be used to describe the propagation of ocean waves, is analytically investigated. With the aid of symbolic computation, ... In this paper, the (2+l)-dimensional generalization of shallow water wave equation, which may be used to describe the propagation of ocean waves, is analytically investigated. With the aid of symbolic computation, we prove that the (2+ l)-dimensional generalization of shallow water wave equation possesses the Palnlev6 property under a certain condition, and its Lax pair is constructed by applying the singular manifold method. Based on the obtained Lax representation, the Darboux transformation (DT) is constructed. The first iterated solution, second iterated solution and a special N-soliton solution with an arbitrary function are derived with the resulting DT. Relevant properties are graphically illustrated, which might be helpful to understanding the propagation processes for ocean waves in shallow water. 展开更多
关键词 (2+1)-dimensional generalization of shallow water wave equation singular manifold method Laxpair Darboux transformation symbolic computation
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Exact Periodic Wave Solution of Extended(2+1)-Dimensional Shallow Water Wave Equation with Generalized D_-operators
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作者 董焕河 张艳锋 《Communications in Theoretical Physics》 SCIE CAS CSCD 2015年第4期401-405,共5页
With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dpˉ-operators in term of the Hirota direct method ... With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dpˉ-operators in term of the Hirota direct method when the appropriate value of pˉ is determined. Furthermore, the resulting approach is applied to solve the extended(2+1)-dimensional Shallow Water Wave equation, and the periodic wave solution is obtained and reduced to soliton solution via asymptotic analysis. 展开更多
关键词 (2+1)-dimensional shallow water wave equation Dpˉ-operators binary Bell polynomials Riemann theta function
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Study of abundant explicit wave solutions of the Drinfeld-Sokolov-Satsuma-Hirota(DSSH)equation and the shallow water wave equation
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作者 H.M.Shahadat Ali M.Mamun Miah M.Ali Akbar 《Propulsion and Power Research》 SCIE 2018年第4期320-328,共9页
In this article,the two variable(G'G,1/G)-expansion method is suggested to investigate new and further general multiple exact wave solutions to the Drinfeld-Sokolov-Satsuma-Hirota(DSSH)equation and the shallow wat... In this article,the two variable(G'G,1/G)-expansion method is suggested to investigate new and further general multiple exact wave solutions to the Drinfeld-Sokolov-Satsuma-Hirota(DSSH)equation and the shallow water wave equation which arise in mathematical physics with the aid of computer algebra software,like Mathematica.Three functions and the rational functions solution are found.The method demonstrates power,reliability and efficiency.Indeed,the method is the generalization of the well-known(G/G)-expansion method established by Wang et al.and the method also presents a wider applicability for conducting nonlinear wave equations. 展开更多
关键词 Explicit wave solutions Computer algebra software Drinfeld-Sokolov-Satsuma-Hirota(DSSH)equation shallow water wave equation SOLITON
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Abundant closed form wave solutions to some nonlinear evolution equations in mathematical physics 被引量:3
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作者 M.Mamun Miah Aly R.Seadawy +1 位作者 H.M.Shahadat Ali M.Ali Akbar 《Journal of Ocean Engineering and Science》 SCIE 2020年第3期269-278,共10页
The propagation of waves in dispersive media,liquid flow containing gas bubbles,fluid flow in elastic tubes,oceans and gravity waves in a smaller domain,spatio-temporal rescaling of the nonlinear wave motion are delin... The propagation of waves in dispersive media,liquid flow containing gas bubbles,fluid flow in elastic tubes,oceans and gravity waves in a smaller domain,spatio-temporal rescaling of the nonlinear wave motion are delineated by the compound Korteweg-de Vries(KdV)-Burgers equation,the(2+1)-dimensional Maccari system and the generalized shallow water wave equation.In this work,we effectively derive abundant closed form wave solutions of these equations by using the double(G′/G,1/G)-expansion method.The obtained solutions include singular kink shaped soliton solutions,periodic solution,singular periodic solution,single soliton and other solutions as well.We show that the double(G′/G,1/G)-expansion method is an efficient and powerful method to examine nonlinear evolution equations(NLEEs)in mathematical physics and scientific application. 展开更多
关键词 Close form solutions KdV-Burgers equation The(2+1)-dimensional Maccari system The generalized shallow water wave equation
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RATIONAL FORM SOLITARY WAVE SOLUTIONS FOR SOME TYPES OF HIGH ORDER NONLINEAR EVOLUTION EQUATIONS
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作者 韩廷武 卓相来 《Annals of Differential Equations》 2000年第4期315-319,共5页
In this paper, three types of nonlinear evolution equations such as (2n + 1)th order KdV equation, etc, are studied. And their solitary wave solutions of rational form obtained are available and possess the simplest f... In this paper, three types of nonlinear evolution equations such as (2n + 1)th order KdV equation, etc, are studied. And their solitary wave solutions of rational form obtained are available and possess the simplest form so far. At last, the Hamiltonian form of (2n + 1)th order general KdV equation is generalized. 展开更多
关键词 KdV equation K-P equation model equation for shallow water waves solitary wave solution?
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