On shifted periodic solutions of two nonlinear equations

Xian-jing Lai and Jie-fang Zhang

Chaos, Solitons & Fractals, 2005, vol. 23, issue 4, 1399-1404

Abstract: Using the linear superposition approach, we find periodic solutions with shifted periods and velocities of the (2+1)-dimensional modified Zakharov–Kuznetsov equation and the (3+1)-dimensional Kadomtsev–Petviashvili equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure of generating solutions of nonlinear evolution equations is successful as a consequence of some cyclic identities satisfied by the Jacobi elliptic functions which reduce by 2 (or a larger even number) the degree of cyclic homogeneous polynomials in Jacobi elliptic functions.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:23:y:2005:i:4:p:1399-1404

DOI: 10.1016/j.chaos.2004.06.042

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