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

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posted on 2023-06-08, 06:21 authored by Konstantin BlyussKonstantin Blyuss, TJ Bridges, G Derks
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Physical Review E

ISSN

1539-3755

Publisher

American Physical Society

Issue

5

Volume

67

Department affiliated with

  • Mathematics Publications

Notes

Part 2

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

First Open Access (FOA) Date

2016-03-22

First Compliant Deposit (FCD) Date

2016-11-16

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