The NLS(n, n) equation: Multi-hump compactons and their stability and interaction scenarios

Abstract

Abstract The nonlinear Schrodinger (NLS) equation with fully nonlinear dispersion (called NLS(m, n) equation) has been introduced by Yan [Phys. Lett. A 355 (2006) 212] and shown to possess the single-hump compactons for m = n > 1 . In this paper, we further investigated the focusing NLS(n, n) equation and find that it possesses the multi-hump compactons for n > 1, whose properties are analyzed in detail. Particularly, we surprisedly find that the maximal intensities of the multi-hump compactons approach to the natural base e as n → 1 + . Moreover, we numerically study the stabilities and interactions of the single-hump and double-hump compactons such that some stable multi-hump compactons and elastic interactions are found for some small values of the parameter n. These multi-hump compactons will be useful for understanding the soliton-like solutions and applying them in the related fields of nonlinear science.