Application of the Weierstrass Elliptic Expansion Method to the Long-Wave and Short-Wave Resonance Interaction System

2008 ◽  
Vol 63 (5-6) ◽  
pp. 273-279 ◽  
Author(s):  
Xian-Jing Lai ◽  
Jie-Fang Zhang ◽  
Shan-Hai Mei
Keyword(s):  
Periodic Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Short Wave ◽  
Resonance Interaction ◽  
Solitary Wave Solutions ◽  
Jacobian Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
Long Wave ◽  
Wave Resonance

With the aid of symbolic computation, nine families of new doubly periodic solutions are obtained for the (2+1)-dimensional long-wave and short-wave resonance interaction (LSRI) system in terms of the Weierstrass elliptic function method. Moreover Jacobian elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.

Elliptic Function Solutions of (2+1)-dimensional Longwave – Shortwave Resonance Interaction Equation via a sinh-Gordon Expansion Method

2004 ◽  
Vol 59 (1-2) ◽  
pp. 23-28 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Elliptic Function ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Short Wave ◽  
Resonance Interaction ◽  
Jacobi Elliptic Function ◽  
Wave Resonance ◽  
Trigonometric Function Solutions ◽  
Interaction Equation ◽  
Pacs 02.30

With the aid of symbolic computation, the sinh-Gordon equation expansion method is extended to seek Jacobi elliptic function solutions of (2+1)-dimensional long wave-short wave resonance interaction equation, which describe the long and short waves propagation at an angle to each other in a two-layer fluid. As a result, new Jacobi elliptic function solutions are obtained. When the modulus m of Jacobi elliptic functions approaches 1, we also deduce the singular oliton solutions; while when the modulus m→0, we get the trigonometric function solutions. - PACS: 02.30.Jr, 03.40.Kf

scholarly journals Dynamics of solitons in multicomponent long wave–short wave resonance interaction system

Pramana ◽  
2015 ◽  
Vol 84 (3) ◽  
pp. 327-338 ◽  
Author(s):  
T KANNA ◽  
K SAKKARAVARTHI ◽  
M VIJAYAJAYANTHI ◽  
M LAKSHMANAN
Keyword(s):  
Short Wave ◽  
Resonance Interaction ◽  
Long Wave ◽  
Interaction System ◽  
Wave Resonance

scholarly journals Dynamics of lumps and dark–dark solitons in the multi-component long-wave–short-wave resonance interaction system

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170627 ◽  
Author(s):  
Jiguang Rao ◽  
Kuppuswamy Porsezian ◽  
Jingsong He ◽  
Thambithurai Kanna
Keyword(s):  
Mixed Type ◽  
Dark Soliton ◽  
Short Wave ◽  
Higher Order ◽  
Resonance Interaction ◽  
Rational Solutions ◽  
Dark Solitons ◽  
Long Wave ◽  
Interaction System ◽  
Wave Resonance

General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave–short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N ( N ≥2) lumps annihilating into or producing from N -dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.

Interaction of the variable-coefficient long-wave–short-wave resonance interaction equations

2019 ◽  
Vol 33 (01) ◽  
pp. 1850426
Author(s):  
Hui-Xian Jia ◽  
Da-Wei Zuo
Keyword(s):  
Gravity Waves ◽  
Acoustic Waves ◽  
Variable Coefficient ◽  
Soliton Solutions ◽  
Short Wave ◽  
Resonance Interaction ◽  
Bilinear Method ◽  
Ion Acoustic Waves ◽  
Long Wave ◽  
Wave Resonance

Long-wave–short-wave resonance interaction (LSRI) equations have been studied in the plasmas, gravity waves, nonlinear electron-plasma and ion-acoustic waves. By virtue of the bilinear method, two soliton solutions of the variable-coefficient LSRI equations are attained. Interaction of the solitons are studied when the coefficients are taken as the generalized Gauss functions. New types of the soliton interaction are exhibited. Position and width of the disturbances can be controlled.

scholarly journals NOTE ON THE TWO-COMPONENT ANALOGUE OF TWO-DIMENSIONAL LONG WAVE – SHORT WAVE RESONANCE INTERACTION SYSTEM

2009 ◽  
Vol 51 (A) ◽  
pp. 129-135 ◽  
Author(s):  
KEN-ICHI MARUNO ◽  
YASUHIRO OHTA ◽  
MASAYUKI OIKAWA
Keyword(s):  
Surface Wave ◽  
Wave Packets ◽  
Resonant Interaction ◽  
Short Wave ◽  
Resonance Interaction ◽  
Two Dimensional ◽  
Interfacial Wave ◽  
Long Wave ◽  
Wave Resonance ◽  
Two Component

AbstractAn integrable two-component analogue of the two-dimensional long wave – short wave resonance interaction (2c-2d-LSRI) system is studied. Wronskian solutions of 2c-2d-LSRI system are presented. A reduced case, which describes resonant interaction between an interfacial wave and two surface wave packets in a two-layer fluid, is also discussed.

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