Exploration of novel solitary waves in presence of higher order polynomial nonlinearity and spatio-temporal dispersion via itô calculus

This study investigates highly stochastic solitary waves inside the structure of nonlinear Schrödinger equation of eighth-order, characterized by heightened polynomial nonlinearity and influenced by multiplicative white noise modeled in the Itô sense. To discern the influence of white noise on the governing model, the bright and dark soliton profiles are generated by using the Sardar sub-equation and G ′ / ( b G ′ + G + a ) -expansion methods. Our approach yields diverse solutions, encompassing singular solitary waves, breather, periodic, and dark–bright solitons. Visual representations through 3 D and 2 D graphs with relevant parameter values enhance the comprehension of results. The distinctive nature of our methods, untested in this context, results in novel soliton solutions, underscoring their efficacy. This research not only deepens understanding in soliton wave theory but also demonstrates its practical relevance for solving nonlinear complexities in engineering and scientific fields.