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

• Published in: AIMS mathematics Vol. 8; no. 7; pp. 15670 - 15688
• Main Authors: Hong, Baojian, Wang, Jinghan, Li, Chen
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2023
• Subjects: approximate solutions; exact solutions; fractional coupled nonlinear schrödinger equation; homotopy perturbation method; laplace transform; modified kudryashov method
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2023800

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.