Abstract
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′=λG, G′=μW in which λ 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.
Highlights
Nonlinear partial differential equations are statistical structures used to explain a phenomenon happening among us worldwide
Equationsolution (NDSE)as you are shown in Figure 1, In theSolutions above figures, we illustrate periodic soliton brightInsoliton solution
We include graphs to show the physical representation of the wave solutions when the constant
Summary
Nonlinear partial differential equations are statistical structures used to explain a phenomenon happening among us worldwide. G = 1, and A, B, C are nonzero constants this method equivalent to the Riccati expansion function method [4,5]. From Facts 1–5, theoretically, the transformed rational function method [47] gives us a rational function expansion around a solution to an integrable ODE, which is the most general procedure to generate traveling wave solutions. This method is one of the effective and powerful methods to solve nonlinear ODEs. In the proposed method, trial equation is the generalized Riccati ODE (7) or (8), which contains many parameters to get a different type of several traveling wave solutions. The multiple exp-function method [49] aims to solve PDEs, but not integro–differential equations. One-wave and two-wave solutions are computed in [49], since N wave solutions, for example, N-soliton solutions need more elaborate theoretical consideration [50]
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