A Linearized Implicit Scheme for Solving Logarithmic Nonlinear Schrödinger’s Equation

Abstract

In this research, we will develop a numerical scheme for solving the nonlinear logarithmic Schrödinger’s equation using the Linearized implicit scheme, that has second-order accuracy in space and time, with significant savings in computational time. We then compare the results to those obtained previously using the Crank-Nicolson scheme of the finite difference method. The stability and precision of this method will be evaluated before it is implemented. Precise solution and conserved quantities will be used to prove the efficiency as well as reliability of the method that has been proposed. Additionally, tests are conducted to explore the interactions that take place between two and three solitons. The numerical findings of our investigation demonstrated that the behavior of interactions is elastic.