Large-space and large-time asymptotic properties of vector rogon-soliton and soliton-like solutions for n-component NLS equations.

Abstract

In this paper, we analyze the large-space and large-time asymptotic properties of the vector rogon-soliton and soliton-like solutions of the n-component nonlinear Schrödinger equation with mixed nonzero and zero boundary conditions. In particular, we find that these solutions have different decay velocities along different directions of the x axis, that is, the solutions exponentially and algebraically decay along the positive and negative directions of the x axis, respectively. Moreover, we study the change of the acceleration of soliton moving with the increase in time or distance along the characteristic line (i.e., soliton moving trajectory). As a result, we find that the product of the acceleration and distance square tends to some constant value as time increases. These results will be useful to better understand the related multi-wave phenomena and to design physical experiments.