Some new wave solutions and modulation instability of a Hamiltonian amplitude equation in optical fibres

Abstract

The nonlinear Schrödinger equation (NLSE) is one of the most important physical models for explaining the dynamics of optical soliton proliferation in optical fibre theory. Due to an extensive variety of applications for ultrafast signal routing systems and short light pulses in communications, optical soliton propagation in nonlinear fibres is a topic of substantial present interest. To overcome the ill-posedness of the unstable NLSE, a new term Lxt is introduced which leads to the Hamiltonian amplitude equation. In this work, we study exact wave solutions to the nonlinear complex model by utilizing a set of analytical approaches namely as the exp(−ξ(δ)) method, the improved F-expansion technique, and the extended modified auxiliary equation mapping method. Numerous solutions, including singular periodic, multi-periodic, single bell-shaped, and multi-bell-shaped wave frameworks were found. The proposed plan of action is swift, strong, as well as offers the requirements needed to verify the origin of these solutions. Additionally, a dynamics representation of the fascinating behaviour of several solidarity using 2D, 3D, and contour graphs is provided, also we discuss the stability analysis and modulation instability of the proposed model.