On the interaction of solitons for a class of integrable systems in the spacetime \(\mathbb{R}^{n+1}\) (Q1202959)

Multisoliton solutions to \((n+1)\)-dimensional nonlinear PDE's which can be represented in the form of the Lax pair are considered in a general abstract form, without specifying a particular form of the equations. The analysis is based upon the Darboux transformation, which is formulated not directly in terms of the wave variables, but in terms of the wave (Jost) functions, that are inherently related to the Lax-pair representation of the equations considered. It is demonstrated that a one-soliton solution can be obtained as the Darboux transform of the trivial solution; then, it is demonstrated that multisoliton solutions are structured so that collisions of an arbitrary number of solitons are purely elastic, apart from phase shifts.