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New Jacobi Elliptic Functions Solutions for the Combined KdV-MKdV Equation

Dianchen Lu, Qian Shi

Open publisher page 30 citations

Abstract

In this work, we established exact solutions for the combined KdV-MKdV equation. By con- structing four new types of Jacobi elliptic functions solutions, the Jacobi elliptic functions expansion method will be extend. With the aid of symbolic computation system mathematica, obtain some new exact periodic solutions of nonlinear combined KdV-MKdV equation , and these solutions are degenerated to solitary wave solutions and triangle function solutions in the limit case when the modulus of the Jacobi elliptic functions �� → 1 or �� → 0.

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What this paper is about

In this work, we established exact solutions for the combined KdV-MKdV equation. By con- structing four new types of Jacobi elliptic functions solutions, the Jacobi elliptic functions expansion method will be extend. With the aid of symbolic computation system mathematica, obtain some new exact periodic solutions of nonlinear combined KdV-MKdV equation , and these solutions are degenerated to solitary wave solutions and triangle function solutions in the limit case when the modulus of the Jacobi elliptic functions �� → 1 or �� → 0.

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Available abstract

In this work, we established exact solutions for the combined KdV-MKdV equation. By con- structing four new types of Jacobi elliptic functions solutions, the Jacobi elliptic functions expansion method will be extend. With the aid of symbolic computation system mathematica, obtain some new exact periodic solutions of nonlinear combined KdV-MKdV equation , and these solutions are degenerated to solitary wave solutions and triangle function solutions in the limit case when the modulus of the Jacobi elliptic functions �� → 1 or �� → 0.

Key concepts: Elliptic function, Korteweg–de Vries equation, Jacobi elliptic functions, Mathematics, Cnoidal wave, Jacobi method, Elliptic rational functions, Quarter period

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