Analytical study of rational and double-soliton rational solutions governed by the KdV–Sawada–Kotera–Ramani equation with variable coefficients

In this work, we construct rational and double-soliton rational solutions of the KdV–Sawada–Kotera–Ramani equation with variable coefficients by using the unified method and its generalized form. We employ these methods to obtain soliton rational solutions, periodic rational solutions, elliptic rati...

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Bibliographic Details
Published inNonlinear dynamics Vol. 89; no. 3; pp. 2283 - 2289
Main Author Osman, M. S.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2017
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Collision dynamics
Control
Dynamical Systems
Engineering
Korteweg-Devries equation
Mathematical analysis
Mechanical Engineering
Original Paper
Solitary waves
Surface water
Traveling waves
Vibration
Water waves
The KdV–Sawada–Kotera–Ramani equation
The generalized unified method
The unified method
Variable coefficients
Traveling wave solutions
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Summary:In this work, we construct rational and double-soliton rational solutions of the KdV–Sawada–Kotera–Ramani equation with variable coefficients by using the unified method and its generalized form. We employ these methods to obtain soliton rational solutions, periodic rational solutions, elliptic rational solutions, and two-soliton rational solutions. Here, we study the nonlinear interactions between these solutions and the collision between the long surface water waves. Also, we discuss the dynamical behavior of the traveling wave solutions and their structures.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3586-y