MULTIPLE SOLITON SOLUTIONS FOR THREE SYSTEMS OF BROER–KAUP–KUPERSHMIDT EQUATIONS DESCRIBING NONLINEAR AND DISPERSIVE LONG GRAVITY WAVES

2012 ◽  
Vol 26 (20) ◽  
pp. 1250126 ◽  
Author(s):  
ABDUL MAJID WAZWAZ
Keyword(s):  
Gravity Waves ◽  
Soliton Solutions ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Multiple Soliton Solutions ◽  
Simplified Form

Three systems of Broer–Kaup–Kupershmidt (BKK) equations, that describe nonlinear and dispersive long gravity waves, are investigated. The simplified form of the Hirota's bilinear method is employed for a reliable treatment of these three systems. Multiple soliton solutions are formally derived for each system.

Multiple Soliton Solutions for a Variety of Coupled Modified Korteweg–de Vries Equations

2011 ◽  
Vol 66 (10-11) ◽  
pp. 625-631
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Mkdv Equation ◽  
Resonance Phenomenon ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Multiple Soliton Solutions ◽  
De Vries ◽  
Coupled Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

We make use of Hirota’s bilinear method with computer symbolic computation to study a variety of coupled modified Korteweg-de Vries (mKdV) equations. Multiple soliton solutions and multiple singular soliton solutions are obtained for each coupled equation. The resonance phenomenon of each coupled mKdV equation is proved not to exist.

A COMPLETELY INTEGRABLE SYSTEM OF COUPLED MODIFIED KdV EQUATIONS

2010 ◽  
Vol 19 (01) ◽  
pp. 145-151 ◽  
Author(s):  
ABDUL-MAJID WAZWAZ
Keyword(s):  
Integrable System ◽  
Soliton Solutions ◽  
Resonance Phenomenon ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Kdv Equations ◽  
Multiple Soliton Solutions ◽  
Modified Kdv Equations ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

In this work, we study a system of coupled modified KdV (mKdV) equations. Multiple soliton solutions and multiple singular soliton solutions are derived by using the Hirota's bilinear method and the Hietarinta approach. The resonance phenomenon is examined.

Integrability of coupled KdV equations

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Resonance Phenomenon ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Kdv Equations ◽  
Multiple Soliton Solutions ◽  
Coupled Kdv Equations ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

AbstractThe integrability of coupled KdV equations is examined. The simplified form of Hirota’s bilinear method is used to achieve this goal. Multiple-soliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation. The resonance phenomenon of each model will be examined.

Modulational instability and multiple rogue wave solutions for the generalized CBS-BK equation

2021 ◽  
pp. 2150408
Author(s):  
Wang Gang ◽  
Jalil Manafian ◽  
Fatma Berna Benli ◽  
Onur Alp İlhan ◽  
Reza Goldaran
Keyword(s):  
Asymptotic Behavior ◽  
Multiple Solutions ◽  
Modulation Instability ◽  
Rogue Wave ◽  
Modulational Instability ◽  
Soliton Solutions ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Multiple Soliton Solutions

An integrable of the generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky-Konopelchenko (CBS-BK) equation is studied, by employing Hirota’s bilinear method the bilinear form is obtained, and the multiple-soliton solutions are constructed. The modified of improved bilinear method has been utilized to investigate multiple solutions. In addition, some graphs including 3D, contour, density, and [Formula: see text]-curves plots of the addressed equation with specific coefficients are shown. Finally, under certain conditions, the asymptotic behavior of the linearization solution is analyzed to prove that the modulation instability is stable for some points.

Multiple rogue and soliton wave solutions to the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation arising in fluid mechanics and plasma physics

2021 ◽  
pp. 2150383
Author(s):  
Onur Alp Ilhan ◽  
Sadiq Taha Abdulazeez ◽  
Jalil Manafian ◽  
Hooshmand Azizi ◽  
Subhiya M. Zeynalli
Keyword(s):  
Rogue Wave ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
The Novel ◽  
Algebraic Equations ◽  
Bilinear Method ◽  
Dynamical Characteristics ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Soliton Wave Solutions

Under investigation in this paper is the generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt equation. Based on bilinear method, the multiple rogue wave (RW) solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions for the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue wave solutions are obtained via Maple 18 software. The exact lump and RW solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters, will be constructed. Via various three-dimensional plots and density plots, dynamical characteristics of these waves are exhibited.

scholarly journals Painlevé integrability and multisoliton solutions of a generalized KdV system

2020 ◽  
Vol 34 ◽  
pp. 03008
Author(s):  
Pinki Kumari ◽  
R.K. Gupta ◽  
Sachin Kumar
Keyword(s):  
Soliton Solutions ◽  
Painlevé Test ◽  
Bilinear Method ◽  
Multiple Soliton Solutions ◽  
Simplified Bilinear Method ◽  
P Type ◽  
Multisoliton Solutions

The integrability of a generalized KdV model, which has abundant physical applications in many fields, is investigated by employing Painlevé test. Eventually, we discover a new generalized P-type KdV model in sense of WTCKruskal method. Subsequently, Hereman’s simplified bilinear method is used to examine the integrability of the resulted model. As a result, multiple soliton solutions of newly discovered model are formally obtained.

Multiple-soliton solutions for coupled KdV and coupled KP systems

2009 ◽  
Vol 87 (12) ◽  
pp. 1227-1232 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Resonance Phenomenon ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Multiple Soliton Solutions ◽  
Two Systems ◽  
Kp Equations ◽  
Hirota Bilinear ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

In this work we study two systems of coupled KdV and coupled KP equations. The Hirota bilinear method is applied to show that these two systems are completely integrable. Multiple-soliton solutions and multiple singular-soliton solutions are derived for each system. The resonance phenomenon is examined as well.

Multisoliton solutions of a (2+1)-dimensional variable-coefficient Toda lattice equation via Hirota’s bilinear method

2014 ◽  
Vol 92 (3) ◽  
pp. 184-190 ◽  
Author(s):  
Sheng Zhang ◽  
Dong Liu
Keyword(s):  
Variable Coefficient ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Hirota’S Bilinear Method ◽  
Lattice Equation ◽  
Bilinear Method ◽  
Dimensional Variable ◽  
Toda Lattice Equation ◽  
Multisoliton Solutions

In this paper, Hirota’s bilinear method is extended to construct multisoliton solutions of a (2+1)-dimensional variable-coefficient Toda lattice equation. As a result, new and more general one-soliton, two-soliton, and three-soliton solutions are obtained, from which the uniform formula of the N-soliton solution is derived. It is shown that Hirota’s bilinear method can be used for constructing multisoliton solutions of some other nonlinear differential-difference equations with variable coefficients.

Sign in / Sign up

Export Citation Format

Share Document