Rational and semi-rational solutions of the modified Kadomtsev-Petviashvili equation and the (2+1)-dimensional Konopelchenko-Dubrovsky equation

被引：0
作者：
Huang, Shuting [1 ]
Wu, Chengfa [1 ]
Qi, Cheng [2 ]
机构：
[1] Shenzhen Univ, Inst Adv Study, Shenzhen 518060, Peoples R China
[2] Shenzhen Univ, Coll Mechatron & Control Engn, Shenzhen 518060, Peoples R China
来源：
NONLINEAR DYNAMICS | 2019年 / 97卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Rational solutions; Semi-rational solutions; (2+1)-Dimensional Konopelchenko-Dubrovsky equation; Modified Kadomtsev-Petviashvili equation; KP hierarchy reduction method; NONLINEAR SCHRODINGER-EQUATION; GENERAL SOLITON-SOLUTIONS; WAVE SOLUTIONS; EVOLUTION-EQUATIONS; TRANSFORMATIONS; DYNAMICS; ZERO;
D O I：
10.1007/s11071-019-05166-4
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
General rational and semi-rational solutions of the modified Kadomtsev-Petviashvili (mKP) equation and the Konopelchenko-Dubrovsky equation are obtained based on the bilinear method and the KP hierarchy reduction technique. These solutions are expressed in terms of NxN determinants. The dynamics of the solutions, which exhibit various patterns, are thoroughly analyzed. It is shown that the rational solutions may describe the elastic interaction of a single-peak wave with either a double-peak (M-shape) wave or another single-peak wave for N=1. Depending on the choice of parameters, the semi-rational solutions are found to depict the inelastic interaction between two (Y-shape) or three waves for N=1. The second-order (N=2) rational solutions exhibit the elastic interaction of three single-peak waves with either one double-peak wave or another single-peak wave. Inelastic interaction is displayed by proper choices of the parameters for semi-rational solutions. When N>2, similar local dynamical behaviors of the rational and semi-rational solutions have been observed.
引用
收藏
页码：2829 / 2841
页数：13
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