| Citation: |
Panpan Wang, Xiufang Feng, Shangqin He. LIE SYMMETRY REDUCTION FOR (2+1)-DIMENSIONAL FRACTIONAL SCHRÖDINGER EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 502-516. doi: 10.11948/20240133
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LIE SYMMETRY REDUCTION FOR (2+1)-DIMENSIONAL FRACTIONAL SCHRÖDINGER EQUATION
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Abstract
This study investigates Lie symmetry analysis, exact solutions, and conservation laws for a (2+1)-dimensional fractional Schrödinger equation. The original equations have been reduced to fractional ODEs employing the obtained vector field. For the considered equation, exact solutions are also established. Furthermore, the resulting exact solutions are demonstrated for convergence. Conservation laws for this equation have been investigated employing the Ibragimov theorem.
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References
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Panpan Wang, Xiufang Feng, Shangqin He. LIE SYMMETRY REDUCTION FOR (2+1)-DIMENSIONAL FRACTIONAL SCHRÖDINGER EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 502-516. doi: 10.11948/20240133
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Figure 1.
Numerical simulation of power series solutions
$ |q| $ $ a_{0}=b_{0}=a_{1}=b_{1}=0.1 $ $ a-b=-1 $ $ \gamma=0.1 $ $ \alpha=0.8 $ -
Figure 2.
Wave disseminate pattern along
$ y $ $ a_{0}=b_{0}=a_{1}=b_{1}=0.1 $ $ a-b=-1 $ $ \gamma=0.1 $ $ \alpha=0.8 $ $ x=0.2 $