Nonlinear Dynamics of Solitons for the
Vector Modified Korteweg-de Vries
Equation

V. Fenchenko

B. Verkin Institute for Low Temperature Physics and Engineering of the National
Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: vfenchenko@ukr.net

E. Khruslov

B. Verkin Institute for Low Temperature Physics and Engineering of the National
Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: khruslov@ilt.kharkov.ua

Received June 14, 2017, revised September 6, 2017

Abstract

The vector generalization of the modified Korteweg–de Vries equation is considered and the inverse scattering transform for solving this equation is developed. The solitons and the breather solutions are constructed and the processes of their interactions are studied. It is shown that along with one-component soliton solutions, there are three-component solutions which have essentially a three-component structure.