# American Institute of Mathematical Sciences

November  2013, 33(11&12): 4841-4873. doi: 10.3934/dcds.2013.33.4841

## Periodic traveling--wave solutions of nonlinear dispersive evolution equations

 1 Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee, 38152 2 Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, United States

Received  February 2012 Revised  November 2012 Published  May 2013

For a general class of nonlinear, dispersive wave equations, existence of periodic, traveling-wave solutions is studied. These traveling waveforms are the analog of the classical cnoidal-wave solutions of the Korteweg-de Vries equation. They are determined to be stable to perturbation of the same period. Their large wavelength limit is shown to be solitary waves.
Citation: Hongqiu Chen, Jerry L. Bona. Periodic traveling--wave solutions of nonlinear dispersive evolution equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 4841-4873. doi: 10.3934/dcds.2013.33.4841
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