EXPLICIT EXACT PERIODIC WAVE SOLUTIONS AND THEIR LIMIT FORMS FOR A LONG WAVES-SHORT WAVES MODEL

Bin He; Qing Meng

doi:10.11948/2017092

2017 Volume 7 Issue 4

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Bin He, Qing Meng. EXPLICIT EXACT PERIODIC WAVE SOLUTIONS AND THEIR LIMIT FORMS FOR A LONG WAVES-SHORT WAVES MODEL[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1503-1533. doi: 10.11948/2017092

Citation:

Bin He, Qing Meng. EXPLICIT EXACT PERIODIC WAVE SOLUTIONS AND THEIR LIMIT FORMS FOR A LONG WAVES-SHORT WAVES MODEL[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1503-1533. doi: 10.11948/2017092

EXPLICIT EXACT PERIODIC WAVE SOLUTIONS AND THEIR LIMIT FORMS FOR A LONG WAVES-SHORT WAVES MODEL

Bin He¹,
Qing Meng²

1 College of Mathematics, Honghe University, 661199 Mengzi, China;
2 Department of Physics, Honghe University, 661199 Mengzi, China

Fund Project:

Abstract

Abstract

A long waves-short waves model is studied by using the approach of dynamical systems. The sufficient conditions to guarantee the existence of solitary wave, kink and anti-kink waves, and periodic wave in different regions of the parametric space are given. All possible explicit exact parametric representations of above traveling waves are presented. When the energy of Hamiltonian system corresponding to this model varies, we also show the convergence of the periodic wave solutions, such as the periodic wave solutions converge to the solitary wave solutions, kink and anti-kink wave solutions, and periodic wave solutions, respectively
- A long waves-short waves model /
- solitary wave solution /
- kink and anti-kink wave solutions /
- periodic wave solution /
- limit form
MSC: 34C25;34F10;35C07;35C08

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References

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