Multi-Soliton and Rational Solutions for the Extended Fifth-Order KdV Equation in Fluids

被引:3
作者
Meng, Gao-Qing [1 ,2 ]
Gao, Yi-Tian [1 ]
Zuo, Da-Wei [1 ,3 ]
Shen, Yu-Jia [1 ]
Sun, Yu-Hao [1 ]
Yu, Xin [1 ]
机构
[1] Beijing Univ Aeronaut & Astronaut, Minist of Educ, Key Lab Fluid Mech & Natl Lab Computat Fluid Dyna, Beijing 100191, Peoples R China
[2] North China Elect Power Univ, Dept Math & Phys, Baoding 071003, Peoples R China
[3] Shijiazhuang TieDao Univ, Dept Math & Phys, Shijiazhuang 050043, Peoples R China
来源
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES | 2015年 / 70卷 / 07期
基金
中国国家自然科学基金;
关键词
Darboux Transformation; Extended Fifth-Order KdV Equation; Multi-Soliton Solutions; Rational Solutions; Symbolic Computation; SOLITARY WAVE INTERACTION; MAXWELL-BLOCH SYSTEM; BACKLUND TRANSFORMATION; SOLITONS; WATER; ORDER; INTEGRABILITY; BREATHERS;
D O I
10.1515/zna-2015-0131
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
Korteweg-de Vries (KdV)-type equations are used as approximate models governing weakly nonlinear long waves in fluids, where the first-order nonlinear and dispersive terms are retained and in balance. The retained second-order terms can result in the extended fifth-order KdV equation. Through the Darboux transformation (DT), multi-soliton solutions for the extended fifth-order KdV equation with coefficient constraints are constructed. Soliton propagation properties and interactions are studied: except for the velocity, the amplitude and width of the soliton are not influenced by the coefficient of the original equation; the amplitude, velocity, and wave shape of each soltion remain unchanged after the interaction. By virtue of the generalised DT and Taylor expansion of the solutions for the corresponding Lax pair, the first-and second-order rational solutions of the equation are obtained.
引用
收藏
页码:559 / 566
页数:8
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