Lie symmetry analysis and dynamic behaviors for nonlinear generalized Zakharov system
作者： Cheng Chen , Yao-Lin Jiang
DOI: 10.1007/S13324-017-0200-X
关键词: Mathematics 、 Mathematical physics 、 Bifurcation theory 、 Nonlinear system 、 Zakharov system 、 Schrödinger equation 、 Symmetry (physics) 、 Phase portrait 、 Invariant (mathematics) 、 Lie point symmetry
摘要: In this paper Lie symmetry analysis method is applied to study nonlinear generalized Zakharov system which the coupled of Schrodinger equations. With aid point symmetry, reduced into ODEs and some group invariant solutions are obtained where new, not reported in literatures. Then bifurcation theory qualitative employed investigate system. Through phase portraits, Jacobi-elliptic function found, such as periodic-wave solutions, kink-shaped bell-shaped solitary-wave solutions.
springer.com
harvard.edu
sci-hub.se 参考文章(33)
Thierry Cazenave, Semilinear Schrodinger Equations ,(2003)
Peter J. Olver, Applications of Lie Groups to Differential Equations ,(1986)
Tosio Kato, Nonlinear Schrödinger equations Lecture Notes in Physics. ,vol. 345, pp. 218- 263 ,(1989) , 10.1007/3-540-51783-9_22
Emmanuel Yomba, The sub-ODE method for finding exact travelling wave solutions of generalized nonlinear Camassa-Holm, and generalized nonlinear Schrödinger equations Physics Letters A. ,vol. 372, pp. 215- 222 ,(2008) , 10.1016/J.PHYSLETA.2007.03.008
K. R. Raslan, The first integral method for solving some important nonlinear partial differential equations Nonlinear Dynamics. ,vol. 53, pp. 281- 286 ,(2008) , 10.1007/S11071-007-9262-X
Li Ling-Xiao, Wang Ming-Liang, The (G′/G)-expansion method and travelling wave solutions for a higher-order nonlinear schrödinger equation Applied Mathematics and Computation. ,vol. 208, pp. 440- 445 ,(2009) , 10.1016/J.AMC.2008.12.005
M.A. Abdou, The extended F-expansion method and its application for a class of nonlinear evolution equations Chaos Solitons & Fractals. ,vol. 31, pp. 95- 104 ,(2007) , 10.1016/J.CHAOS.2005.09.030
E. V. Krishnan, A. Biswas, Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity by mapping and ansatz methods Physics of Wave Phenomena. ,vol. 18, pp. 256- 261 ,(2010) , 10.3103/S1541308X10040059
Yubin Zhou, Mingliang Wang, Yueming Wang, Periodic wave solutions to a coupled KdV equations with variable coefficients Physics Letters A. ,vol. 308, pp. 31- 36 ,(2003) , 10.1016/S0375-9601(02)01775-9