Analytical solutions to a class of fractional coupled nonlinear Schrödinger equations via Laplace-HPM technique

Baojian Hong; Jinghan Wang; Chen Li; Baojian Hong; Jinghan Wang; Chen Li

doi:10.3934/math.2023800

AIMS Mathematics

2023, Volume 8, Issue 7: 15670-15688. doi: 10.3934/math.2023800

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Analytical solutions to a class of fractional coupled nonlinear Schrödinger equations via Laplace-HPM technique

1.
Faculty of Mathematical Physics, Nanjing Institute of Technology, Nanjing 211167, China
2.
Faculty of Electric Power Engineering, Nanjing Institute of Technology, Nanjing 211167, China
3.
Faculty of Architectural Engineering, Nanjing Institute of Technology, Nanjing 211167, China

Received: 24 February 2023 Revised: 03 April 2023 Accepted: 11 April 2023 Published: 27 April 2023
MSC : 65Mxx, 34A08

In this article, a class of fractional coupled nonlinear Schrödinger equations (FCNLS) is suggested to describe the traveling waves in a fractal medium arising in ocean engineering, plasma physics and nonlinear optics. First, the modified Kudryashov method is adopted to solve exactly for solitary wave solutions. Second, an efficient and promising method is proposed for the FCNLS by coupling the Laplace transform and the Adomian polynomials with the homotopy perturbation method, and the convergence is proved. Finally, the Laplace-HPM technique is proved to be effective and reliable. Some 3D plots, 2D plots and contour plots of these exact and approximate solutions are simulated to uncover the critically important mechanism of the fractal solitary traveling waves, which shows that the efficient methods are much powerful for seeking explicit solutions of the nonlinear partial differential models arising in mathematical physics.
- fractional coupled nonlinear Schrödinger equation,
- modified Kudryashov method,
- Laplace transform,
- Homotopy perturbation method,
- exact solutions,
- approximate solutions
Citation: Baojian Hong, Jinghan Wang, Chen Li. Analytical solutions to a class of fractional coupled nonlinear Schrödinger equations via Laplace-HPM technique[J]. AIMS Mathematics, 2023, 8(7): 15670-15688. doi: 10.3934/math.2023800

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Abstract

In this article, a class of fractional coupled nonlinear Schrödinger equations (FCNLS) is suggested to describe the traveling waves in a fractal medium arising in ocean engineering, plasma physics and nonlinear optics. First, the modified Kudryashov method is adopted to solve exactly for solitary wave solutions. Second, an efficient and promising method is proposed for the FCNLS by coupling the Laplace transform and the Adomian polynomials with the homotopy perturbation method, and the convergence is proved. Finally, the Laplace-HPM technique is proved to be effective and reliable. Some 3D plots, 2D plots and contour plots of these exact and approximate solutions are simulated to uncover the critically important mechanism of the fractal solitary traveling waves, which shows that the efficient methods are much powerful for seeking explicit solutions of the nonlinear partial differential models arising in mathematical physics.

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