The exact and numerical solutions for a dual-waveguide lattice laser radiation with linear gain and nonlinear losses

Abstract In this research, the Laser Radiation Propagation in a Dual-Waveguide Lattice with linear gain and nonlinear losses equation (LRPDWL) are considered. The exact solutions of the mentioned model are extracted via two techniques. The first one: is the so-called ( G ′/ G )-Expansion Technique that surrenders to the homogenous balance principle, while the second is the effective numerical and semi-analytic technique called the Differential Transform Technique (DTT). The initial conditions for the Differential Transform Technique emerged from the exact solution achieved by ( G ′/ G ) - Technique ( G ′/ G )-T). The optical properties of dissipative solitons in one-dimensional laser radiation within a dual-waveguide lattice have been investigated for the first time using the Newton iterative method for the proposed model. With an appropriate choice of parameters, a balance between nonlinear losses and linear localized gain can be achieved. Our study introduces new exact solution forms that reveal the optical characteristics of dissipative solitons in the model. Comparing the numerical solution with its corresponding ( G ′/ G ) solution via the absolute error is considered and it shows the agreement between both forms of solutions. The two-dimensional and three-dimensional behavior of all obtained solutions has been simulated and documented using the Mathematica program.