Lump interactions with plane solitons

Abstract

We analyse the detail of interactions of two-dimensional solitary waves called lumps and one-dimensional line solitons within the framework of the Kadomtsev-Petviashvili equation describing wave processes in media with positive dispersion. We show that line solitons can emit or absorb lumps or periodic chains of lumps; they can interact with each other by means of lumps. Within a certain time interval, lumps or lump chains can emerge between two line solitons and disappear then due to absorption by one of the solitons. This phenomenon resembles the appearance of rogue waves in the oceans. The results obtained are graphically illustrated and can be applicable to the description of physical processes occurring in plasma, fluids, solids, nonlinear optical media, and other fields.a This paper was submitted to the special issue of the journal Radiophysics and Quantum Electronics dedicated to the 80-th Birthday of Professor M.I. Rabinovich.

Multi-Solitons, Multi-Breathers and Multi-Rational Solutions of Integrable Extensions of the Kadomtsev–Petviashvili Equation in Three Dimensions

“…The derivation of Equation (1), as well as its Lax pair, is presented in Section 2. Two-dimensional integrable equations, like KP and DS equations, possess a variety of particular solutions, which can be obtained using different techniques, including the inverse scattering method, the d-bar method, the Darboux transformation, the Hirota bilinear method and the KP hierarchy reduction method [21][22][23][24][25][26][27][28][29][30]. In this connection, smooth multi-soliton and high-order breather solutions, as well as high-order rational solutions of Equation (1), are constructed in Sections 3 and 4, respectively, via Hirota's bilinear method.…”