Exploring the chaotic, sensitivity and wave patterns to the dual-mode resonant Schrödinger equation: application in optical engineering

The comprehension of nonlinear problems is essential for the understanding of nonlinear wave propagation in applied sciences. This work investigates the dual-mode manifestation within the nonlinear Schrodinger equation, clarifying the amplification or absorption of coupled waves. This investigation explores the dual-mode phenomenon's simultaneous generation of two distinct waves, which are influenced by three critical parameters: phase velocity, nonlinearity, and dispersive factor. By utilizing the complex wave transformation, we derive the nonlinear ordinary differential equation of the governing model. Additionally, we employ recently developed analytical techniques, including the modified generalized exponential rational function method and the multivariate generalized exponential rational integral function method, to find a wide range of solutions such as bright-dark, bright, dark, and combined solitons for the proposed model. Moreover, the chaotic and sensitivity analysis are discussed. Different graphs are included to clarify the behavior of solutions for several parameter values.