Stochastic Breather and Soliton Dynamics of a Third-Order Complex mKdV (Higher-Order NLS-Type) Equation

This study presents a comprehensive investigation of optical solitary waves governed by a third-order complex modified Korteweg-de Vries (higher-order nonlinear Schrödinger-type, mKdV-NLS) equation incorporating stochastic effects. Initially, the methodology outlines the general procedure of this approach. Subsequently, by applying the traveling waves transformation to the given equation, it is reformulated into nonlinear ordinary differential equations (NLODEs). These NLODEs are then decomposed into their imaginary and real components. Furthermore, the proposed methodology is implemented to derive new solutions for optical solitary waves within the mKdV-NLS type model, encompassing stochastic breather-like waves, singular solitons, periodic waves, and various wave interactions. Additionally, numerical visualizations of the exact analytical solitary waves are provided, facilitating an examination of the stochastic term’s influence on wave dynamics. This study advances the understanding of optical wave behavior and clarifies the effects of stochastic contributions, offering valuable insights for both theoretical studies and practical applications in optics and related fields.