Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics

In this article, we will apply some of the algebraic methods to find great moving solutions to some nonlinear physical and engineering questions, such as a nonlinear (1 + 1) Ito integral differential equation and (1 + 1) nonlinear Schrödinger equation. To analyze practical solutions to these problems, we essentially use the generalized expansion approach. After various $W$ and $G$ options, we get several clear means of estimating the plentiful nonlinear physics solutions. We present a process like-direct expansion process-method of expansion. In the particular case of $W^{\prime }=\lambda G$, $G^{\prime }=\mu W$ in which $\lambda$ and μ are arbitrary constants, we use the expansion process to build some new exact solutions for nonlinear equations of growth if it fulfills the decoupled differential equations.