On the soliton and numerical solutions to the Nurshuak–Tolkynay–Myrzakulov-II-Equation

Abstract

Abstract The Nurshuak–Tolkynay–Myrzakulov-II-Equation, which is (1 + 1)-dimensions integrable equation, considered one of the nonlinear models that very naturally arise inspect dealing with the mean field approximation of many-body systems, including various important phenomena like phase transitions, anomalous diffusion, shock waves, and traveling wave solution. In this article, we will study two various forms of the Nurshuak–Tolkynay–Myrzakulov-II-Equation, which are the complex Nurshuak–Tolkynay–Myrzakulov-II-A-Equation and the real Nurshuak–Tolkynay–Myrzakulov-II-B-Equation. Through our study, we will innovate for the first time the new soliton solutions types for these two models individually. These new innovated soliton solutions types will be derived via a significant universal technique that is prepared for this target, which is the Generalized Kudryashov Technique. To ensure the validity and quality of the innovated soliton solutions types, we will utilize the Haar Wavelet Technique to construct identical numerical solutions for all innovative soliton solutions. The initial conditions needed to apply the Haar Wavelet Technique are derived from the obtained soliton solutions. The 2D, 3D graphs simulations that show the soliton behavior dynamic characterizes this model have been constructed not only for the semi-analytical technique but also with its corresponding numerical technique.