Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrodinger equation

摘要

In this paper, a simple and constructive method is presented to find thegeneralized perturbation (n,M)-fold Darboux transformations (DTs) of themodified nonlinear Schrodinger (MNLS) equation in terms of fractional forms ofdeterminants. In particular, we apply the generalized perturbation (1,N-1)-foldDTs to find its explicit multi-rogue-wave solutions. The wave structures ofthese rogue-wave solutions of the MNLS equation are discussed in detail fordifferent parameters, which display abundant interesting wave structures,including the triangle and pentagon, etc. and may be useful to study thephysical mechanism of multirogue waves in optics. The dynamical behaviors ofthese multi-rogue-wave solutions are illustrated using numerical simulations.The same Darboux matrix can also be used to investigate the Gerjikov-Ivanovequation such that its multi-rogue-wave solutions and their wave structures arealso found. The method can also be extended to find multi-rogue-wave solutionsof other nonlinear integrable equations.