Pure and Applied Mathematics Quarterly

Volume 11 (2015)

Number 2

Traveling wave-front solutions with small oscillations at infinity for a KdV6 equation under a small perturbation

Pages: 293 – 314

DOI: https://dx.doi.org/10.4310/PAMQ.2015.v11.n2.a6

Authors

Shengfu Deng (Department of Mathematics, Lingnan Normal University, Zhanjiang, Guangdong, China)

Yuzhen Mi (Department of Mathematics, Lingnan Normal University, Zhanjiang, Guangdong, China)

Abstract

This paper studies the traveling wave solutions of a KdV6 equation under a small perturbation. Applying the dynamical system approach, we rigorously prove that this equation has a new wave solution—wave-front solution with small non-decaying oscillations at infinity (called thereafter generalized wave-front solution).

Keywords

KdV6 equation, wave-front solution, homoclinic solution, periodic solution

2010 Mathematics Subject Classification

Primary 34C37, 35B32. Secondary 34C25, 74J35.

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Published 24 August 2016