New dark, bright, one-soliton, bell-shape and anti-bell shape solutions of the LPD model with two forms of nonlinearity

Abstract

This paper is focused with the investigation of new exact analytical solutions to two types of nonlinearities of the Lakshmanan–Porsezian–Daniel models, namely anti-cubic law and cubic-quintic law of nonlinearity. To achieve the diverse wave patterns to the considered model, a novel method, namely the new Kudryashov technique, is used. The newly accomplished solutions exhibit many types of wave solutions such as one-soliton, bright, dark, bell-shape and anti-bell shape solutions. The dynamics of the derived solutions are represented by three-dimensional (3D) and two-dimensional (2D) graphs. The novel aspect of this study is the balance between dispersion and nonlinear phenomena, which have not been achieved in previous studies. Based on these solutions, the fiber structure can be designed to improve its quality. Furthermore, this shows the method’s ability to solve various forms of nonlinear complex phenomena and produce other solitary wave solutions.