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New Exact Solutions for the Combined KdV and mKdV Equation

Dianchen Lu

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Abstract

In this paper,based on the generalized Jacobi elliptic functions expansion method,we obtain abundant exact explicit solutions of the combined KdV(cKdV) and modified KdV(mKdV) equation,these solutions are degenerated to the solitary wave solutions and the triangle function solutions in the limit cases when the modulus of the Jacobian elliptic functions m→1 or 0,which shows that the new method is more powerful to seek the exact solutions of the nonlinear partial differential equations in mathematical physics.

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What this paper is about

In this paper,based on the generalized Jacobi elliptic functions expansion method,we obtain abundant exact explicit solutions of the combined KdV(cKdV) and modified KdV(mKdV) equation,these solutions are degenerated to the solitary wave solutions and the triangle function solutions in the limit cases when the modulus of the Jacobian elliptic functions m→1 or 0,which shows that the new method is more powerful to seek the exact solutions of the nonlinear partial differential equations in mathematical physics.

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Available abstract

In this paper,based on the generalized Jacobi elliptic functions expansion method,we obtain abundant exact explicit solutions of the combined KdV(cKdV) and modified KdV(mKdV) equation,these solutions are degenerated to the solitary wave solutions and the triangle function solutions in the limit cases when the modulus of the Jacobian elliptic functions m→1 or 0,which shows that the new method is more powerful to seek the exact solutions of the nonlinear partial differential equations in mathematical physics.

Key concepts: Korteweg–de Vries equation, Elliptic function, Mathematics, Jacobi elliptic functions, Jacobian matrix and determinant, Limit (mathematics), Partial differential equation, Nonlinear system

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