Integrability and Exact Solutions for a (2+1)-dimensional Variable-Coefficient KdV Equation

By using the WTC method and symbolic computation, we apply the Painlevé test for a (2+1)-dimensional variable-coefficient Kortweg-de Vries (KdV) equation, and the considered equation is found to possess the Painlevé property without any parametric constraints. The auto-Bǎcklund transformation and several types of exact solutions are obtained by using the Painlevé truncated expansion method. Finally, the Hirota’s bilinear form is presented and multi-soliton solutions are also constructed

Conservation laws for a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We find the Lie point symmetries of a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model. Then we establish its quasi self-adjointness and corresponding conservation laws. (C) 2012 Elsevier B.V. All rights reserved.We find the Lie point symmetries of a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model. Then we establish its quasi self-adjointness and corresponding conservation laws18511271135FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [2011/05855-9]Government of Russian Federation [11.G34.31.0042, 220]2011/05855–9SEM INFORMAÇÃ

Conservation Laws For A Coupled Variable-coefficient Modified Korteweg-de Vries System In A Two-layer Fluid Model

We find the Lie point symmetries of a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model. Then we establish its quasi self-adjointness and corresponding conservation laws. © 2012 Elsevier B.V.18511271135Zhu, S.H., Gao, Y.T., Sun, Z.Y., Gai, X.L., Meng, D.X., Painlevé property, soliton-like solutions and complexitons for a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model (2010) Appl Math Comput, 217, pp. 295-307Gao, Y., Tang, X.Y., A coupled variable coefficient modified KdV equation arising from a two-layer fluid system (2007) Commun Theor Phys, 48, pp. 961-970Ibragimov, N., A new conservation theorem (2007) J Math Anal Appl, 333, pp. 311-328Ibragimov, N., Nonlinear self-adjointness and conservation laws (2011) J Phys A: Math Theor, 44 (4320), p. 02Ibragimov, N., Nonlinear self-adjointness in constructing conservation laws (2011) Arch ALGA, pp. 1-90Wolfram Reasearch, Inc (2010), Mathematica edition: Version 8.0. Champaign, Illinois, Wolfram Reasearch, IncDimas, S., Partial differential equations, algebraic computing and nonlinear systems Ph.D. ThesisUniversity of Patras, Patras, Greece, 2008Dimas, S., Tsoubelis, D., SYM: a new symmetry-finding package for Mathematica (2005) The 10th international conference in modern group analysis, pp. 64-70. , University of Cyprus, Nicosia, N. Ibragimov, C. Sophocleous, P. Damianou (Eds.)Dimas, S., Tsoubelis, D., A new Mathematica-based program for solving overdetermined systems of PDEs (2006) Applied Mathematica, electronic proceedings of the eighth international Mathematica symposium (IMS'06), , INRIA, Avignon, France, Y. Papegay (Ed.)Ibragimov, N., Transformation groups applied to mathematical physics (2001) Mathematics and its applications, , SpringerOlver, P.J., Applications of Lie groups to differential equations (2000) Graduate texts in mathematics, 107. , Springer, New Yor