Lie symmetry analysis and exact solutions of space-time fractional cubic Schrodinger equation

作者：Yu, Jicheng; Feng, Yuqiang^*

来源：INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2022, 19(05): 2250077.

DOI：10.1142/S0219887822500773

• Lie symmetry analysis
• space-time fractional cubic Schrodinger equation
• Riemann-Liouville fractional derivative
• Erdelyi-Kober fractional derivative
• exact solution

In this paper, the Lie symmetry analysis method is applied to the space-time fractional cubic Schrodinger equation. The group generators are obtained for the system of space-time fractional differential equations. They are utilized to reduce the system of fractional partial differential equations with Riemann-Liouville fractional derivative to the system of fractional ordinary differential equations with Erdelyi-Kober fractional derivative. Then, the power series method is applied to derive explicit solutions for the reduced systems. Furthermore, the traveling wave solutions of the integer-order cubic Schrodinger equation is obtained.