Lie Symmetry Analysis, Power Series Solutions and Conservation Laws of (2+1)-Dimensional Time Fractional Modified Bogoyavlenskii–Schiff Equations

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED
Jicheng Yu, Yuqiang Feng
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引用次数: 0

Abstract

In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional modified Bogoyavlenskii–Schiff equations, which is an important model in physics. The one-dimensional optimal system composed by the obtained Lie symmetries is utilized to reduce the system of (2+1)-dimensional fractional partial differential equations with Riemann–Liouville fractional derivative to the system of (1+1)-dimensional fractional partial differential equations with Erdélyi–Kober fractional derivative. Then the power series method is applied to derive explicit power series solutions for the reduced system. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.

(2+1)-Dimensional Time Fractional Modified Bogoyavlenskii-Schiff Equations 的列对称分析、幂级数解和守恒定律
本文将李对称分析方法应用于物理学中的一个重要模型--(2+1)维时间分数修正博戈亚夫伦斯基-希夫方程。利用所得到的李对称性组成的一维最优系统,将具有黎曼-刘维尔分导数的 (2+1)- 维分式偏微分方程系统还原为具有埃尔德利-科贝尔分导数的 (1+1)- 维分式偏微分方程系统。然后,应用幂级数方法推导出简化系统的显式幂级数解。此外,还发展了新守恒定理和诺特算子广义,以构建所研究方程的守恒定律。
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来源期刊
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
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