The exact solutions for the nonlinear variable-coefficient fifth-order Schrödinger equation

• Published in: Results in physics Vol. 39; p. 105708
• Main Authors: Li, Cheng’ao, Lu, Junliang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2022; Elsevier
• Subjects: Jacobian elliptic function expansion method; Modified traveling wave transformation; Nonlinear variable-coefficient Schrödinger equation; Traveling wave solution; 35A08; Modified traveling wave transformation; 35G20; 35A24; Jacobian elliptic function expansion method; Nonlinear variable-coefficient Schrödinger equation; 35C08; Traveling wave solution; 35C07
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2022.105708

In the paper, the nonlinear variable-coefficient fifth-order Schrödinger (NLVS) equation is researched. The NLVS equation is an integrable equation, which can be described the spreading of ultrashort pulses in an inhomogeneous optical fiber. Firstly, by using the modified traveling wave transformation, the NLVS equation is changed into an ordinary equation. Secondly, by the Jacobian elliptic function expansion method for the ordinary equation, we obtain the exact solutions for the ordinary equation, and then, we obtain the exact solutions to the NLVS equation. These solutions mainly include three types: Jacobi elliptic function solutions, hyperbolic function solutions, and triangular function solutions. Finally, according to the special parameters, we show the figures of the exact solutions. •By the modified traveling wave transformation method, we obtain new explicit solutions for the nonlinear variable-coefficient fifth-order Schrödinger equation.•There exist mainly trigonometric function, hyperbolic function, and rational function traveling wave solutions.•Physically, we explain all the solutions, which include compacton, soliton, cuspon, and peakon traveling waves.