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2006•Journal of Sichuan Normal UniversityRequires access

New Periodic Solutions to the Nonlinear Equations with Jacobi Elliptic Functions

Jian Zhang

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Abstract

Based on Jacobi elliptic function method which is proposed by Liu S.S.,et al(Acta Phys.Sin.,2001,50(11):2068-2072.),we applied the modified Jacobi elliptic function method to construct a new exact periodic solutions of modified BBM equation and combined KdV-mKdV equation.These periodic solutions obtained by this method can be reduced to the corresponding solitary wave solutions under the limit condition.This method can also be applied to other nonlinear equations.

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What this paper is about

Based on Jacobi elliptic function method which is proposed by Liu S.S.,et al(Acta Phys.Sin.,2001,50(11):2068-2072.),we applied the modified Jacobi elliptic function method to construct a new exact periodic solutions of modified BBM equation and combined KdV-mKdV equation.These periodic solutions obtained by this method can be reduced to the corresponding solitary wave solutions under the limit condition.This method can also be applied to other nonlinear equations.

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Available abstract

Based on Jacobi elliptic function method which is proposed by Liu S.S.,et al(Acta Phys.Sin.,2001,50(11):2068-2072.),we applied the modified Jacobi elliptic function method to construct a new exact periodic solutions of modified BBM equation and combined KdV-mKdV equation.These periodic solutions obtained by this method can be reduced to the corresponding solitary wave solutions under the limit condition.This method can also be applied to other nonlinear equations.

Key concepts: Elliptic function, Jacobi elliptic functions, Korteweg–de Vries equation, Mathematics, Cnoidal wave, Elliptic integral, Nonlinear system, Mathematical analysis

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