A modified approach for a reliable study of new nonlinear equation: two-mode Korteweg–de Vries–Burgers equation

Marwan Alquran; H. M. Jaradat; Muhammed I. Syam

doi:10.1007/s11071-017-3968-1

A modified approach for a reliable study of new nonlinear equation: two-mode Korteweg–de Vries–Burgers equation

Marwan Alquran, H. M. Jaradat, Muhammed I. Syam

Department of Mathematical Sciences

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

40 Citations (Scopus)

Abstract

In this paper, we establish a new nonlinear equation which is called the two-mode Korteweg–de Vries–Burgers equation (TMKdV–BE). The new equation describes the propagation of two different wave modes simultaneously. First, we introduce a new Cole–Hopf transformation needed for the modified simplified bilinear method to find necessary conditions on the solution of TMKdV–BE. Also, a finite series in terms of tanh–coth function is presented as an alternative method to study the solution of the equation. Finally, the reliability of the obtained results is discussed in the last section.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Nonlinear Dynamics
DOIs	https://doi.org/10.1007/s11071-017-3968-1
Publication status	Accepted/In press - Dec 2 2017

Keywords

Simplified bilinear method
Tanh–coth expansion method
Two-mode KdV–Burgers equation

ASJC Scopus subject areas

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

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10.1007/s11071-017-3968-1

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abstract = "In this paper, we establish a new nonlinear equation which is called the two-mode Korteweg–de Vries–Burgers equation (TMKdV–BE). The new equation describes the propagation of two different wave modes simultaneously. First, we introduce a new Cole–Hopf transformation needed for the modified simplified bilinear method to find necessary conditions on the solution of TMKdV–BE. Also, a finite series in terms of tanh–coth function is presented as an alternative method to study the solution of the equation. Finally, the reliability of the obtained results is discussed in the last section.",

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AU - Alquran, Marwan

AU - Jaradat, H. M.

AU - Syam, Muhammed I.

PY - 2017/12/2

Y1 - 2017/12/2

N2 - In this paper, we establish a new nonlinear equation which is called the two-mode Korteweg–de Vries–Burgers equation (TMKdV–BE). The new equation describes the propagation of two different wave modes simultaneously. First, we introduce a new Cole–Hopf transformation needed for the modified simplified bilinear method to find necessary conditions on the solution of TMKdV–BE. Also, a finite series in terms of tanh–coth function is presented as an alternative method to study the solution of the equation. Finally, the reliability of the obtained results is discussed in the last section.

AB - In this paper, we establish a new nonlinear equation which is called the two-mode Korteweg–de Vries–Burgers equation (TMKdV–BE). The new equation describes the propagation of two different wave modes simultaneously. First, we introduce a new Cole–Hopf transformation needed for the modified simplified bilinear method to find necessary conditions on the solution of TMKdV–BE. Also, a finite series in terms of tanh–coth function is presented as an alternative method to study the solution of the equation. Finally, the reliability of the obtained results is discussed in the last section.

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KW - Tanh–coth expansion method

KW - Two-mode KdV–Burgers equation

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A modified approach for a reliable study of new nonlinear equation: two-mode Korteweg–de Vries–Burgers equation

Abstract

Keywords

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