PhysRevE.67.056626.pdf (175.55 kB)
Transverse instability and its long-term development for solitary waves of the (2+1)-dimensional Boussinesq equation
journal contribution
posted on 2023-06-08, 06:21 authored by Konstantin BlyussKonstantin Blyuss, TJ Bridges, G DerksThe 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.
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Physical Review EISSN
1539-3755Publisher
American Physical SocietyExternal DOI
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5Volume
67Department affiliated with
- Mathematics Publications
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Part 2Full text available
- Yes
Peer reviewed?
- Yes
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2012-02-06First Open Access (FOA) Date
2016-03-22First Compliant Deposit (FCD) Date
2016-11-16Usage metrics
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