Bifurcation analysis and exact solutions for a class of generalized time-space fractional nonlinear Schrödinger equations

Baojian Hong; Baojian Hong

doi:10.3934/mbe.2023643

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 14377-14394. doi: 10.3934/mbe.2023643

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Bifurcation analysis and exact solutions for a class of generalized time-space fractional nonlinear Schrödinger equations

Baojian Hong ^,

Faculty of Mathematical Physics, Nanjing Institute of Technology, Nanjing 211167, China

Academic Editor: Jose M. Rodriguez

Received: 15 April 2023 Revised: 22 June 2023 Accepted: 25 June 2023 Published: 30 June 2023

In this work, we focus on a class of generalized time-space fractional nonlinear Schrödinger equations arising in mathematical physics. After utilizing the general mapping deformation method and theory of planar dynamical systems with the aid of symbolic computation, abundant new exact complex doubly periodic solutions, solitary wave solutions and rational function solutions are obtained. Some of them are found for the first time and can be degenerated to trigonometric function solutions. Furthermore, by applying the bifurcation theory method, the periodic wave solutions and traveling wave solutions with the corresponding phase orbits are easily obtained. Moreover, some numerical simulations of these solutions are portrayed, showing the novelty and visibility of the dynamical structure and propagation behavior of this model.
- time-space fractional nonlinear Schrödinger equation,
- general mapping deformation method,
- Caputo fractional derivative,
- bifurcation,
- exact solutions
Citation: Baojian Hong. Bifurcation analysis and exact solutions for a class of generalized time-space fractional nonlinear Schrödinger equations[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 14377-14394. doi: 10.3934/mbe.2023643

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Abstract

In this work, we focus on a class of generalized time-space fractional nonlinear Schrödinger equations arising in mathematical physics. After utilizing the general mapping deformation method and theory of planar dynamical systems with the aid of symbolic computation, abundant new exact complex doubly periodic solutions, solitary wave solutions and rational function solutions are obtained. Some of them are found for the first time and can be degenerated to trigonometric function solutions. Furthermore, by applying the bifurcation theory method, the periodic wave solutions and traveling wave solutions with the corresponding phase orbits are easily obtained. Moreover, some numerical simulations of these solutions are portrayed, showing the novelty and visibility of the dynamical structure and propagation behavior of this model.

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