Resonant collisions among localized waves in the (2+1)-dimensional Hirota–Satsuma–Ito equation

Abstract

In this paper, we study the resonant collisions among different types of localized solitary waves in the (2+1)-dimensional Hirota–Satsuma–Ito equation, which are described by N-soliton solutions constructed using bilinear method. Through the asymptotic analysis and limit treatment of the phase shift of these localized waves, the elastic collisions among different localized waves can be transformed into resonant collisions. Hereby, we study the resonant collision between a breather/ lump and a bright line soliton and find two collision situations: (i) the breather is semi-localized in space and the shape of the breather is not localized during the propagation and (ii) the lump wave generates from the bright line wave. At the same time, we investigate the resonant collision between a breather/lump and two bright line solitons. In these evolution processes, we also gain two dynamical behaviors: (iii) the breather is always localized in space and the shape of the breather is not localized during the propagation, and (iv) the lump wave appears from a bright line soliton and then disappears into the other bright line soliton. Localized wave and interaction solutions of the nonlinear wave models have a great impact on oceanography and physics. The results may be useful in researching the physical phenomena in shallow water waves and nonlinear optics.