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On the solutions and conservation laws of the ( 1 + 1 ) -dimensional higher-order Broer-Kaup system

Chaudry Masood Khalique

Author Affiliations

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho, 2735, Republic of South Africa

Boundary Value Problems 2013, 2013:41  doi:10.1186/1687-2770-2013-41

Published: 28 February 2013

Abstract

In this paper we obtain exact solutions of the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/41/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/41/mathml/M1">View MathML</a>-dimensional higher-order Broer-Kaup system which was obtained from the Kadomtsev-Petviashvili equation by the symmetry constraints. The methods used to determine the exact solutions of the underlying system are the Lie group analysis and the simplest equation method. The solutions obtained are the solitary wave solutions. Moreover, we derive the conservation laws of the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/41/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/41/mathml/M1">View MathML</a>-dimensional higher-order Broer-Kaup system by employing the multiplier approach and the new conservation theorem.

Keywords:
the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/41/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/41/mathml/M1">View MathML</a>-dimensional higher-order Broer-Kaup system; integrability; Lie group analysis; simplest equation method; solitary waves; conservation laws