Constructions of the soliton solutions to coupled nonlinear Schrödinger equation with advanced mathematical techniques

Abstract

In our research paper, we explore the application of mathematical techniques, both analytical and numerical, to solve the coupled nonlinear Schrödinger equation. To obtain accurate solutions, we use the improved, modified, extended tanh-function method. By breaking down the Schrödinger equation into real and imaginary components, we derive four interconnected equations. We analyze these equations using the generalized tanh method to find precise solutions. This set of equations is of great importance in quantum mechanics and helps us understand the behavior of quantum systems. We provide an analytical and numerical solution using the implicit finite difference. Our method is second-order in both space and time, and we have verified its stability through von Neumann’s stability analysis.

Optical Solitons with Differential Group Delay and Inter-Modal Dispersion Singlet

“…Unlike previous studies that primarily focused on mathematical techniques for solving the coupled nonlinear Schrödinger equation [1], our research explores the practical implications of soliton propagation interacting with differential group delay. While prior work relied on the improved, modified, and extended tanh-function method to derive accurate solutions for quantum systems, our study adopts three innovative approaches to uncover new soliton solutions amidst inter-modal dispersion.…”

“…They provide valuable insights into soliton dynamics across diverse scenarios and parameter regimes, thereby enhancing our understanding of their behavior. A wide range of approaches was implemented in the past to study various nonlinear dynamical structures more proficiently [1][2]. Analytical techniques strive to locate exact mathematical solutions to nonlinear evolution equations (NLEEs), even if they are rendered non-integrable through the Painleve test.…”