Exact travelling wave solutions for nonlinear system of spatiotemporal fractional quantum mechanics equations

Abstract

Schrödinger equation is an indispensable model for quantum mechanics, used for modelling several fascinating complex nonlinear physical systems, such as quantum condensates, nonlinear optics, hydrodynamics, shallow-water waves, and the harmonic oscillator. The objective of this paper is to investigate and study the exact travelling wave solutions of nonlinear triple fractional Schrödinger equations involving a modified Riemann–Liouville fractional derivative. Using the Riccati-Bernoulli Sub-ODE technique, the Bäcklund transformation is employed to handle the posed system. The traveling wave solutions methodology lies in converting the fractional Schrödinger equations into a nonlinear system of fractional ODEs. An infinite sequence of solutions to the fractional partial differential equations can be obtained directly through solving the resulting nonlinear fractional system. Some graphical representations of the obtained solutions after selecting suitable values for fractional values and parameters are illustrated to test accuracy and verify the power, and effectiveness of the proposed method.

Keywords

• Traveling wave method
• Bäcklund transformation
• Fractional Schrödinger equation
• Riemann–Liouville derivative
• Quantum mechanics