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Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system

Bury, Rhys, Mikhailov, Alexander V., Wang, Jing Ping (2017) Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system. Physica D: Nonlinear Phenomena, 347 . pp. 21-41. ISSN 0167-2789. (doi:10.1016/j.physd.2017.01.003) (KAR id:55062)

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In the paper we develop the dressing method for the solution of the two-dimensional periodic Volterra system with a period N. We derive soliton solutions of arbitrary rank k and give a full classification of rank 1 solutions. We have found a new class of exact solutions corresponding to wave fronts which represent smooth interfaces between two nonlinear periodic waves or a periodic wave and a trivial (zero) solution. The wave fronts are non-stationary and they propagate with a constant average velocity. The system also has soliton solutions similar to breathers, which resembles soliton webs in the KP theory. We associate the classification of soliton solutions with the Schubert decomposition of the Grassmannians View the MathML source and View the MathML source.

Item Type: Article
DOI/Identification number: 10.1016/j.physd.2017.01.003
Subjects: Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Jing Ping Wang
Date Deposited: 19 Apr 2016 22:06 UTC
Last Modified: 16 Feb 2021 13:34 UTC
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Wang, Jing Ping:
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