Smooth Exact Traveling Wave Solutions Determined by Singular Nonlinear Traveling Wave Systems: Two Models

被引：3
作者：
Li, Jibin [1 ,2 ]
Chen, Guanrong [3 ]
Deng, Shengfu [1 ]
机构：
[1] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China
[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
[3] City Univ Hong Kong, Dept Elect Engn, Kowloon, Hong Kong, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2019年 / 29卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Integrable system; exact solution; homoclinic orbit; heteroclinic orbit; periodic solution; Green-Naghdi equation; Raman soliton model; SOLITONS; EQUATIONS; WATER;
D O I：
10.1142/S0218127419500470
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For a singular nonlinear traveling wave system of the first class, if there exist two node points of the associated regular system in the singular straight line, then the dynamics of the solutions of the singular system will be very complex. In this paper, two representative nonlinear traveling wave system models (namely, the traveling wave system of Green-Naghdi equations and the traveling wave system of the Raman soliton model for optical metamaterials) are investigated. It is shown that, if there exist two node points of the associated regular system in the singular straight line, then the singular system has no peakon, periodic peakon and compacton solutions, but rather, it has smooth periodic wave, solitary wave and kink wave solutions.
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页数：13
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