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Dynamics of Strongly Nonlinear Kinks and Solitons in a Two‐Layer Fluid
Author(s) -
Gorshkov K.,
Ostrovsky L. A.,
Soustova I.
Publication year - 2011
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2010.00497.x
Subject(s) - nonlinear system , soliton , perturbation (astronomy) , limiting , physics , classical mechanics , dynamics (music) , perturbation theory (quantum mechanics) , mathematical analysis , mathematical physics , mathematics , quantum mechanics , mechanical engineering , acoustics , engineering
Perturbation theory is developed for interaction of strongly nonlinear solitary waves close to the limiting, tabletop solitons (Π‐solitons). The method is based on representing each soliton as a compound of two kinks so that the interaction of N solitons is treated as the interaction of 2 N kinks. As an example the Miyata–Choi–Camassa equations for a two‐layer fluid is considered. Equations for kink coordinates are obtained and analyzed. Some nontrivial features of two‐soliton interaction characteristic of the strongly nonlinear case are established.