A study on the two-mode coupled modified Korteweg–de Vries using the simplified bilinear and the trigonometric-function methods

Muhammed Syam; H. M. Jaradat; Marwan Alquran

doi:10.1007/s11071-017-3732-6

A study on the two-mode coupled modified Korteweg–de Vries using the simplified bilinear and the trigonometric-function methods

Muhammed Syam, H. M. Jaradat, Marwan Alquran

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

48 Citations (Scopus)

Abstract

In this paper, we study the system of the two-mode coupled mKdV using the simplified bilinear method. We find the necessary conditions that make the solutions exists. In addition, we investigate the multiple soliton and multiple singular soliton solutions of this system. We find the necessary conditions to have N-soliton solutions. To verify the efficiency of our approach, we apply the trigonometric-function methods. The trigonometric-function methods produce 27 different solutions to this system. These solutions are the same solutions that are produced by the simplified bilinear method. Up to our knowledge, this study is new and we can apply the same idea to the other coupled systems.

Original language	English
Pages (from-to)	1363-1371
Number of pages	9
Journal	Nonlinear Dynamics
Volume	90
Issue number	2
DOIs	https://doi.org/10.1007/s11071-017-3732-6
Publication status	Published - Oct 1 2017

Keywords

N-soliton solutions
Simplified bilinear method
Singular soliton solutions
System of the two-mode coupled mKdV
Trigonometric-function method

ASJC Scopus subject areas

Control and Systems Engineering
Aerospace Engineering
Ocean Engineering
Mechanical Engineering
Electrical and Electronic Engineering
Applied Mathematics

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10.1007/s11071-017-3732-6

Cite this

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abstract = "In this paper, we study the system of the two-mode coupled mKdV using the simplified bilinear method. We find the necessary conditions that make the solutions exists. In addition, we investigate the multiple soliton and multiple singular soliton solutions of this system. We find the necessary conditions to have N-soliton solutions. To verify the efficiency of our approach, we apply the trigonometric-function methods. The trigonometric-function methods produce 27 different solutions to this system. These solutions are the same solutions that are produced by the simplified bilinear method. Up to our knowledge, this study is new and we can apply the same idea to the other coupled systems.",

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PY - 2017/10/1

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A study on the two-mode coupled modified Korteweg–de Vries using the simplified bilinear and the trigonometric-function methods

Abstract

Keywords

ASJC Scopus subject areas

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