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Transverse instability and its long-term development for solitary waves of the (2 + 1) -dimensional Boussinesq equation

Blyuss, K. B., Bridges, T. J. and Derks, G. (2003) Transverse instability and its long-term development for solitary waves of the (2 + 1) -dimensional Boussinesq equation Physical Review E.

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Abstract

The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multisymplectic formulation of this equation gives an explicit relation between the parameters for transverse instability when the transverse wave number is small. The Evans function is then computed explicitly, giving the eigenvalues for the transverse instability for all transverse wave numbers. To determine the nonlinear and long-time implications of the transverse instability, numerical simulations are performed using pseudospectral discretization. The numerics confirm the analytic results, and in all cases studied, the transverse instability leads to collapse.

Item Type: Article
Additional Information: Published in Physical Review E, 67, 056626. © 2003 The American Physical Society.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:42
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1546

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