SINGULAR PERIODIC WAVES OF AN INTEGRABLE EQUATION FROM SHORT CAPILLARY-GRAVITY WAVES

Chunhai Li; Shengqiang Tang; Wentao Huang; Feng Zhao

doi:10.11948/2017063

2017 Volume 7 Issue 3

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Chunhai Li, Shengqiang Tang, Wentao Huang, Feng Zhao. SINGULAR PERIODIC WAVES OF AN INTEGRABLE EQUATION FROM SHORT CAPILLARY-GRAVITY WAVES[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1013-1021. doi: 10.11948/2017063

Citation:

Chunhai Li, Shengqiang Tang, Wentao Huang, Feng Zhao. SINGULAR PERIODIC WAVES OF AN INTEGRABLE EQUATION FROM SHORT CAPILLARY-GRAVITY WAVES[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1013-1021. doi: 10.11948/2017063

SINGULAR PERIODIC WAVES OF AN INTEGRABLE EQUATION FROM SHORT CAPILLARY-GRAVITY WAVES

1 School of Mathematics and Computing Science, School of Information and Communication, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, China;
2 Department of Science, Guilin University of Aerospace Technology, Guilin, Guangxi, 541004, China

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Abstract

Abstract

The effects of parabola singular curves in the integrable nonlinear wave equation are studied by using the bifurcation theory of dynamical system. We find new singular periodic waves for a nonlinear wave equation from short capillary-gravity waves. The new periodic waves possess weaker singularity than the periodic peakon. It is shown that the second derivatives of the new singular periodic wave solutions do not exist in countable number of points but the first derivatives exist. We show that there exist close connection between the new singular periodic waves and parabola singular curve in phase plane of traveling wave system for the first time.
- Bifurcation theory of dynamical systems /
- peakon /
- periodic peakon /
- periodic wave /
- parabola singular curve
MSC: 34A05;35C08;37K40;74J35;35Q51

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