New multi-wave solutions of the conformable LPD model with nonlinear wave phenomena arise in mathematical physics

Abstract

In this paper, the conformable Lakshmanan–Porsezian–Daniel equation with parabolic law nonlinearity is solved and the newly acquired optical solutions are analysed. To achieve this, two robust analytical techniques are implemented namely, the three-wave method and the interaction phenomena form. The newly obtained solutions are in the form of dark, w-shaped, periodic, peakon, bright and three-soliton solutions and their interaction solution in a kinky base. These characteristics are analysed by the graphical representation which demonstrates the reliability and virtue of the proposed methods. The most fascinating part of the reported solutions is their use in science and engineering. The novel aspect of this study is the obtained solutions, which were not before achieved and demonstrate a good balance between the nonlinear physical components. Furthermore, the solutions can facilitate estimating the performance of wave patterns in fibers when needed in a design.