Exact solutions and conservation laws of Zakharov–Kuznetsov modified equal width equation with power law nonlinearity

Nonlinear Analysis: Real World Applications - Tập 13 Số 4 - Trang 1692-1702 - 2012
Khadijo Rashid Adem1, Chaudry Masood Khalique1
1International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa

Tóm tắt

Từ khóa


Tài liệu tham khảo

Biswas, 2009, 1-soliton solution of the generalized Zakharov–Kuznetsov modified equal width equation, Appl. Math. Lett., 22, 1775, 10.1016/j.aml.2009.06.015

Biswas, 2009, Topological and non-topological solitons for the generalized Zakharov–Kuznetsov modified equal width equation, Int. J. Theor. Phys., 48, 2698, 10.1007/s10773-009-0060-8

Biswas, 2010, Solitary wave solution of the Zakharov–Kuznetsov equation in plasmas with power law nonlinearity, Nonlinear Anal. Real World Appl., 11, 3272, 10.1016/j.nonrwa.2009.08.007

Xu, 2009, Evaluation of two-dimensional ZK-MEW equation using the Exp-function method, Comput. Math. Appl., 58, 2307, 10.1016/j.camwa.2009.03.021

Wazwaz, 2008, The extended tanh method for the Zakharov–Kuznetsov (ZK) equation, the modified ZK equation, and its generalized forms, Commun. Nonlinear Sci. Numer. Simul., 13, 1039, 10.1016/j.cnsns.2006.10.007

Wazwaz, 2005, A class of nonlinear fourth order variant of a generalized Camassa–Holm equation with compact and noncompact solutions, Appl. Math. Comput., 165, 485, 10.1016/j.amc.2004.04.029

Bluman, 1989, Symmetries and Differential Equations, vol. 81

Olver, 1993, Applications of Lie Groups to Differential Equations, vol. 107

Ovsiannikov, 1982

Kudryashov, 2005, Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos Solitons Fractals, 24, 1217, 10.1016/j.chaos.2004.09.109

Kudryashov, 2005, Exact solitary waves of the Fisher equation, Phys. Lett. A, 342, 99, 10.1016/j.physleta.2005.05.025

Ibragimov, 2007, A new conservation theorem, J. Math. Anal. Appl., 333, 311, 10.1016/j.jmaa.2006.10.078

Anco, 2002, Direct construction method for conservation laws of partial differential equations, part I: examples of conservation law classifications, European J. Appl. Math., 13, 545, 10.1017/S095679250100465X

Hereman, 2006, Symbolic computation of conservation laws of nonlinear partial differential equations in multi-dimensions, Int. J. Quant. Chem., 106, 278, 10.1002/qua.20727

Vitanov, 2010, Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity, Commun. Nonlinear Sci. Numer. Simul., 15, 2050, 10.1016/j.cnsns.2009.08.011

Vitanov, 2010, Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics, Commun. Nonlinear Sci. Numer. Simul., 15, 2836, 10.1016/j.cnsns.2009.11.029

Ibragimov, 1994, vol. 1–3

Atherton, 1975, On the existence and formulation of variational principles for nonlinear differential equations, Studies Appl. Math., 54, 31, 10.1002/sapm197554131

Anthonyrajah, 2010, Conservation laws and invariant solutions in the Fanno model for turbulent compressible flow, Math. Comput. Appl., 15, 529