Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/2073
Title: Solitary wave solution of nonlinear multi-dimensional wave equation by bilinear transformation method
Authors: Tanoğlu, Gamze
Keywords: Wave equations
Bilinear transformation method
Nonlinear PDE
Partial differential equations
Solitary waves
Vector wave equation
Issue Date: Oct-2007
Publisher: Elsevier Ltd.
Source: Tanoğlu, G. (2007). Solitary wave solution of nonlinear multi-dimensional wave equation by bilinear transformation method. Communications in Nonlinear Science and Numerical Simulation, 12(7), 1195-1201. doi:10.1016/j.cnsns.2005.12.006
Abstract: The Hirota method is applied to construct exact analytical solitary wave solutions of the system of multi-dimensional nonlinear wave equation for n-component vector with modified background. The nonlinear part is the third-order polynomial, determined by three distinct constant vectors. These solutions have not previously been obtained by any analytic technique. The bilinear representation is derived by extracting one of the vector roots (unstable in general). This allows to reduce the cubic nonlinearity to a quadratic one. The transition between other two stable roots gives us a vector shock solitary wave solution. In our approach, the velocity of solitary wave is fixed by truncating the Hirota perturbation expansion and it is found in terms of all three roots. Simulations of solutions for the one component and one-dimensional case are also illustrated.
URI: http://doi.org/10.1016/j.cnsns.2005.12.006
http://hdl.handle.net/11147/2073
ISSN: 1007-5704
1007-5704
1878-7274
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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