On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

Abstract

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

Keywords

• (2+1) dimensional kdv-mkdv equation
• travelling wave solutions
• jacobi elliptic functions
• conservation laws
• multiplier method
• 02.30.jr
• 02.30.hq
• 04.20.jb