Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/1967
Title: Vector shock soliton and the Hirota bilinear method
Authors: Pashaev, Oktay
Tanoğlu, Gamze
Pashaev, Oktay
Tanoğlu, Gamze
Izmir Institute of Technology. Mathematics
Keywords: Mathematical models
Nonlinear equations
Perturbation techniques
Problem solving
Hirota bilinear methods
Issue Date: Oct-2005
Publisher: Elsevier Ltd.
Source: Pashaev, O., and Tanoǧlu, G. (2005). Vector shock soliton and the Hirota bilinear method. Chaos, Solitons & Fractals, 26(1), 95-105. doi:10.1016/j.chaos.2004.12.021
Abstract: The Hirota bilinear method is applied to find an exact shock soliton solution of the system reaction-diffusion equations for n-component vector order parameter, with the reaction part in form of the third order polynomial, determined by three distinct constant vectors. The bilinear representation is derived by extracting one of the vector roots (unstable in general), which allows us reduce the cubic nonlinearity to a quadratic one. The vector shock soliton solution, implementing transition between other two roots, as a fixed points of the potential from continuum set of the values, is constructed in a simple way. In our approach, the velocity of soliton is fixed by truncating the Hirota perturbation expansion and it is found in terms of all three roots. Shock solitons for extensions of the model, by including the second order time derivative term and the nonlinear transport term are derived. Numerical solutions illustrating generation of solitary wave from initial step function, depending of the polynomial roots are given.
URI: http://doi.org/10.1016/j.chaos.2004.12.021
http://hdl.handle.net/11147/1967
ISSN: 0960-0779
0960-0779
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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