# A Variety of New Solitary-Solutions for the Two-mode Modified Korteweg-de Vries Equation

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

In this paper, we studied the nonlinear two-mode modified Korteweg-de Vries (TMmKdV) equation. We derived multiple singular soliton solutions to this new version of KdV equation by using the simplified form of Hirota's direct method. Also, kink and periodic solutions are extracted by using the tanh-expansion and the sine-cosine function methods. Finally, graphical analysis is conducted to show some physical features regarding TMmKdV equation.

Original language English 88-96 9 Nonlinear Dynamics and Systems Theory 19 1 Published - 1 Jan 2019

### Fingerprint

Solitary Solution
Korteweg-de Vries equation
Modified Equations
Korteweg-de Vries Equation
Hirota Method
KdV Equation
Kink
Soliton Solution
Solitons
Direct Method
Periodic Solution
Graphics
Form

### Keywords

• Hirota bilinear method
• Kink
• Multiple singular solutions
• Periodic solutions
• Sine-cosine function method
• Two-mode mKdV

### ASJC Scopus subject areas

• Mathematical Physics
• Applied Mathematics

### Cite this

A Variety of New Solitary-Solutions for the Two-mode Modified Korteweg-de Vries Equation. / Jaradat, A.; Noorani, M. S.M.; Alquran, M.; Jaradat, H. M.

In: Nonlinear Dynamics and Systems Theory, Vol. 19, No. 1, 01.01.2019, p. 88-96.

Research output: Contribution to journalArticle

@article{361abbbf54e046078cffa5b43feb32b6,
title = "A Variety of New Solitary-Solutions for the Two-mode Modified Korteweg-de Vries Equation",
abstract = "In this paper, we studied the nonlinear two-mode modified Korteweg-de Vries (TMmKdV) equation. We derived multiple singular soliton solutions to this new version of KdV equation by using the simplified form of Hirota's direct method. Also, kink and periodic solutions are extracted by using the tanh-expansion and the sine-cosine function methods. Finally, graphical analysis is conducted to show some physical features regarding TMmKdV equation.",
keywords = "Hirota bilinear method, Kink, Multiple singular solutions, Periodic solutions, Sine-cosine function method, Two-mode mKdV",
author = "A. Jaradat and Noorani, {M. S.M.} and M. Alquran and Jaradat, {H. M.}",
year = "2019",
month = "1",
day = "1",
language = "English",
volume = "19",
pages = "88--96",
journal = "Nonlinear Dynamics and Systems Theory",
issn = "1562-8353",
publisher = "Informath Publishing Group",
number = "1",

}

TY - JOUR

T1 - A Variety of New Solitary-Solutions for the Two-mode Modified Korteweg-de Vries Equation

AU - Noorani, M. S.M.

AU - Alquran, M.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper, we studied the nonlinear two-mode modified Korteweg-de Vries (TMmKdV) equation. We derived multiple singular soliton solutions to this new version of KdV equation by using the simplified form of Hirota's direct method. Also, kink and periodic solutions are extracted by using the tanh-expansion and the sine-cosine function methods. Finally, graphical analysis is conducted to show some physical features regarding TMmKdV equation.

AB - In this paper, we studied the nonlinear two-mode modified Korteweg-de Vries (TMmKdV) equation. We derived multiple singular soliton solutions to this new version of KdV equation by using the simplified form of Hirota's direct method. Also, kink and periodic solutions are extracted by using the tanh-expansion and the sine-cosine function methods. Finally, graphical analysis is conducted to show some physical features regarding TMmKdV equation.

KW - Hirota bilinear method

KW - Kink

KW - Multiple singular solutions

KW - Periodic solutions

KW - Sine-cosine function method

KW - Two-mode mKdV

UR - http://www.scopus.com/inward/record.url?scp=85070880602&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070880602&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85070880602

VL - 19

SP - 88

EP - 96

JO - Nonlinear Dynamics and Systems Theory

JF - Nonlinear Dynamics and Systems Theory

SN - 1562-8353

IS - 1

ER -