One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada–Kotera equation

The main concern of the present article is to study the fifth-order variable-coefficient Sawada–Kotera (VcSK) equation which describes the motion of long waves in shallow water under the gravity. A single- and double-soliton rational solutions for this model are formally retrieved through the genera...

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Bibliographic Details
Published inNonlinear dynamics Vol. 96; no. 2; pp. 1491 - 1496
Main Author Osman, M. S.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2019
Springer Nature B.V
Subjects
Amplitudes
Automotive Engineering
Classical Mechanics
Coefficients
Control
Dynamical Systems
Engineering
Inelastic collisions
Mathematics
Mechanical Engineering
Original Paper
Partial differential equations
Shallow water
Solitary waves
Vibration
Waveguides
Generalized unified method
Fifth-order variable-coefficient Sawada–Kotera equation
35G99
33F10
Inelastic collision
Solitons
35Q51
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Summary:The main concern of the present article is to study the fifth-order variable-coefficient Sawada–Kotera (VcSK) equation which describes the motion of long waves in shallow water under the gravity. A single- and double-soliton rational solutions for this model are formally retrieved through the generalized unified method. For a single-soliton wave, the velocity, the amplitude and the shape of the wave cannot be affected by variable coefficients. There is an inelastic collision (the collision that makes change in amplitude of the soliton waves and shifts in their trajectories) between the double-soliton waves due to the time-varying field in a graded-index waveguide. It hoped that the established solutions can be used to enrich the dynamic behaviors of the VcSK equation.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-019-04866-1