Dynamics of Strongly Nonlinear Solitons and Kinks in a Two-Layer Fluid

Dynamics of Strongly Nonlinear Solitons and Kinks in a Two-Layer Fluid

L. A. Ostrovsky
Zel Technologies/NOAA Earth Systems Research Laboratory

Perturbation theory is developed for interaction of strongly nonlinear solitary waves (solitons) which are close to limiting (tabletop) solitons for which the direct perturbation method representing solitons as classical particles (Gorshkov and Ostrovsky, Phys. D, 1981) is not directly applicable. The method, first suggested by Gorshkov et al (Phys. Rev. E, 2004) for the integrable Gardner equation, is based on representing each soliton as a compound of two well separated kinks of opposite polarities, and considering the interaction of the kinks which belong either to the same or to the neighboring solitons. As an example the Miyata-Choi-Camassa (MCC) equations for strongly nonlinear, long internal waves in a two-layer fluid are analyzed. Approximate equations for kink coordinates are obtained and analyzed. As a result it is demonstrated that the method is not limited by integrability of basic equations, and some non-trivial features of two-soliton interaction are established.