Analytical solutions to the fractional Lakshmanan-Porsezian-Daniel model

Abstract

A new local fractional-order derivative operator is introduced and the Lakshmanan-Porsezian-Daniel (LPD) model is interpreted via this operator. New analytical solutions to the LPD equation is presented by Jacobi elliptic functions and an anzatz method. The complex-valued LPD equation includes a nonlinear term which is considered from three different cases: Kerr, parabolic and anti-cubic law of nonlinearities. For each case, dark, bright, singular optical soliton solutions related with optical fibers are presented. Simulations representing behavior of these solutions for different parameter values are provided.