Exact Traveling Wave Solutions of the Krichever-Novikov Equation: A Dynamical System Approach

被引：1

作者：

Kou, KitIan ^{[1
]}

Li, Jibin ^{[2
]}

机构：

[1] Univ Macau, Dept Math, Macau, Peoples R China

[2] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2017年 / 27卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Integrable system; solitary wave solution; periodic wave solution; quasi-periodic wave solutions; Krichever-Novikov equation; SYMMETRIES;

D O I：

10.1142/S0218127417500584

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show that to find the traveling wave solutions for the Krichever-Novikov equation, we only need to consider a spatial form F-VI of the fourth-order differential equations in the polynomial class having the Painleve property given by [Cosgrove, 2000]. By using the method of dynamical systems to analyze the dynamical behavior of the traveling wave solutions in some two-dimensional invariant manifolds, various exact solutions such as solitary wave solution, periodic wave solutions, quasi-periodic wave solutions and uncountably infinitely many unbounded wave solutions are obtained.

引用

页数：11

共 16 条

[1]

Adler VE, 1998, INT MATH RES NOTICES, V1998, P1

[2]

Anco S. C., 2016, J PHYS A, V49

[3]

[Anonymous], 1983, Sov. Math. Dokl

[4]

[Anonymous], 1979, SOV MATH DOKL

[5] Symmetry reductions and traveling wave solutions for the Krichever-Novikov equation [J].