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

2022/02/23 by Jicheng Yu, Yuqiang Feng · 1 voice
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · doi:10.1142/s0219887822500773

openalex publication_date 2022/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/17

Abstract

In this paper, the Lie symmetry analysis method is applied to the space-time fractional cubic Schrödinger 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 Erdélyi–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 Schrödinger equation is obtained.

Citations

• Fractional Differential Equations

Discussions

• Exploring the fractional cubic Schrödinger equation with Lie symmetry analysis! Group generators reduce complex fractional PDEs to solvable ODEs, leading to explicit solutions and traveling waves: do [bsky, 1 points, 0 comments]

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