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Approximate Solution of Space-Time Fractional KdV Equation and Coupled KdV Equations

15 Jan 2020-Journal of the Physical Society of Japan (The Physical Society of Japan)-Vol. 89, Iss: 1, pp 014002
TL;DR: In this paper, the main goal is to find the approximate solution of the space-time fractional order KdV (STFKdV) equation and Coupled kdV equation by using Homotopy analysis method (HAM).
Abstract: The main goal of this article is to find the approximate solution of the space-time fractional order KdV (STFKdV) equation and Coupled KdV (STFCKdV) equations by using Homotopy analysis method (HAM...
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TL;DR: In this article, a coupled Schrodinger-Boussinesq equation with conformable derivative is presented, which has lots of applications in laser and plasma, and the said equations are reduced to a coupled stationary form using complex travelling wave transformation.
Abstract: This work oversees with the coupled Schrodinger–Boussinesq equations with conformable derivative, which have lots of applications in laser and plasma. The said equations are reduced to a coupled stationary form using complex travelling wave transformation. Next Painleve test applied to derived the integrable cases of the reduced equation, after that using RCAM derived the solution of reduced equations integrable and nonintegrable cases. Few theorems have been presented and proved to ensure their boundedness. All presented boundedness cases have been checked and explained by plotting the solutions for particulars values of parameters satisfying them. The obtained solutions of stationary form utilized to derive solutions of the coupled Schrodinger-Boussinesq equations with conformable derivative. The derived solutions have been plotted and explained. From this, it appears that these solutions propagate by maintaining their two-hump, W-shaped, M-shaped solutions shapes.

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TL;DR: In this paper, a coupled Schrodinger-Boussinesq equation with conformable derivative is presented and the derived solutions have been plotted and explained by plotting the solutions for particulars values of parameters satisfying them.
Abstract: This work oversees with the coupled Schrodinger-Boussinesq equations with conformable derivative, which have lots of applications in laser and plasma. The said equations are reduced to a coupled stationary form using complex travelling wave transformation. Next Painleve test applied to derived the integrable cases of the reduced equation, after that using RCAM derived the solution of reduced equations integrable and nonintegrable cases. Few theorems have been presented and proved to ensure their boundedness. All presented boundedness cases have been checked and explained by plotting the solutions for particulars values of parameters satisfying them. The obtained solutions of stationary form utilized to derive solutions of the coupled Schrodinger-Boussinesq equations with conformable derivative. The derived solutions have been plotted and explained. From this, it appears that these solutions propagate by maintaining their two-hump, W-shaped, M-shaped solutions shapes.