Homoclinic breaters, mulitwave, periodic cross-kink and periodic cross-rational solutions for improved perturbed nonlinear Schrödinger's with quadratic-cubic nonlinearity

Abstract

In this work, we study the soliton solutions for the improved perturbed nonlinear Schrödinger's equation (PNLSE) with quadratic-cubic law nonlinearity (QCLN) by utilizing the log transformation and symbolic computation with the ansatz function schemes. We obtain M -shaped rational soliton, double exponential form, periodic cross-kink (PCK), periodic cross-rational (PCR), multi-waves and homoclinic breather approach. We'll show that M -shaped rational solitons with kink and periodic waves have unique structures and highly interesting interactional behavior. Furthermore, we'll discuss the dynamics of obtained solutions with the help of graphs by assigning appropriate values to the parameters.