Painleve Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan - Kundu - Lakshmanan Equation

被引：60
|
作者：
Kudryashov, Nikolay A. [1 ]
Safonova, Dariya V. [1 ]
Biswas, Anjan [1 ,2 ,3 ,4 ]
机构：
[1] Natl Res Nucl Univ MEPhI, Dept Appl Math, Kashirskoe Sh 31, Moscow 115409, Russia
[2] Alabama A&M Univ, Dept Phys Chem & Math, Normal, AL 35762 USA
[3] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia
[4] Tshwane Univ Technol, Dept Math & Stat, ZA-0008 Pretoria, South Africa
来源：
REGULAR & CHAOTIC DYNAMICS | 2019年 / 24卷 / 06期
基金：
俄罗斯科学基金会;
关键词：
Radhakrishnan - Kundu - Laksmanan equation; integrability; traveling waves; general solution; exact solution; OPTICAL SOLITON PERTURBATION; NONLINEAR EVOLUTION-EQUATIONS; ELLIPTIC FUNCTION EXPANSION; TANH-FUNCTION METHOD; 1ST INTEGRALS; GENERAL-SOLUTION; (G'/G)-EXPANSION METHOD; SCHRODINGER-EQUATION; PERIODIC-SOLUTIONS;
D O I：
10.1134/S1560354719060029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper considers the Radhakrishnan - Kundu - Laksmanan (RKL) equation to analyze dispersive nonlinear waves in polarization-preserving fibers. The Cauchy problem for this equation cannot be solved by the inverse scattering transform (IST) and we look for exact solutions of this equation using the traveling wave reduction. The Painleve analysis for the traveling wave reduction of the RKL equation is discussed. A first integral of traveling wave reduction for the RKL equation is recovered. Using this first integral, we secure a general solution along with additional conditions on the parameters of the mathematical model. The final solution is expressed in terms of the Weierstrass elliptic function. Periodic and solitary wave solutions of the RKL equation in the form of the traveling wave reduction are presented and illustrated.
引用
收藏
页码：607 / 614
页数：8
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