Inverse scattering transformation for generalized nonlinear Schrödinger equation

Abstract

Based on the robust inverse scattering method, the high-order rogue wave of generalized nonlinear Schrödinger equation with nonzero boundary is given. Using this method, we only need the elementary Darboux transformation but not with the limit progress, which is more convenient than before. By choosing different parameters c1 and c2 appeared in the Darboux matrix, the 2n and 2n−1 order rogue waves are derived respectively. Furthermore, the general breather is also given with a different spectral parameters.