New solutions of the 2 + 1 dimensional BKP equation through symmetry analysis: source and sink solutions, creation and diffusion of breathers…

Abstract

Making use of the theory of symmetry transformations in PDEs we construct new solutions of a 2 + 1 dimensional integrable model in the BKP hierarchy. First, we analyze its reductions and we obtain a BKP equation independent on time. Starting with a solution of this equation we find a family of solutions of the 2 + 1 dimensional BKP equation. These solutions depend on three arbitrary functions on t. On the other hand, new solutions can also be constructed by applying some elements of the symmetry group to known solutions of the model. We observed that the solutions found by using both approaches describe interesting processes. Among these solutions we present source and sink solutions, solutions describing the creation or the diffusion (or both) of a breather, finite time blow-up processes, finite time source solutions, line solitons and coherent structures moving at arbitrary velocities.