Stochastic Solutions for two Nonlinear Models of Nonlinear Partial Differential Equations in Mathematical Physics

Nonlinear partial differential equations (NPDEs) in applied science provide an appropriate platform for the creation of novel research in the disciplines of applied mathematics and physical sciences. The development of more effective computer and simulation approaches for analysing these equations is extremely important. Researchers can roughly correctly identify themselves from the process described by solving these equations, enabling them to learn about some realities that are difficult to understand by regular observation. Mathematical and computational modelling have aided in the understanding of real-world phenomena observed in quantum mechanics, optical fiber communications, mechanical engineering, plasma physics, fluid mechanics, etc. A stochastic process is an observation at a specific time that results in a random variable. Brownian motion is a stochastic process that is both a martingale and a Markov process. We expect that recent breakthroughs in stochastic calculus via stochastic partial differential equations (SPDEs) will establish the framework for thoroughly modeling real-world models. Mathematicians, more than anybody else, are most at ease applying SPDEs and stochastic processes to natural models. We will investigate the impact of different stochastic types on the behaviour of the offered solutions. Random effects were found to modify the intensity of the energy wave or the collapse produced by model medium turbulence. Using Matlab software, various profile pictures are given to describe the behaviour of the dynamics for the offered solutions.