一类Hamilton-Jacobi型方程的群分析

IF 1.1 Q1 MATHEMATICS

JOURNAL OF INTERDISCIPLINARY MATHEMATICS Pub Date : 2023-01-01 DOI:10.47974/jim-1646

Jervin Zen Lobo

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引用次数: 0

摘要

本文将李群理论应用于一类一阶非线性偏微分方程——Hamilton-Jacobi型方程。然后利用局部逆定理建立了该方程的李不变条件。然后利用这个条件得到了决定方程。对得到的方程进行拆分和求解，得到所研究方程的对称性。我们得到了最大的可解李代数。得到了对称代数，并对该方程进行了群分类。进一步，推导出一些精确解，并用图形表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Group analysis of a Hamilton–Jacobi type equation

In this paper, we apply Lie group theory to a Hamilton-Jacobi type equation, which is a nonlinear partial differential equation of the first order. We then employ the local inverse theorem to build the Lie invariance condition for this equation. The determining equations are then obtained by using this condition. We split and solve these obtained equations to obtain the symmetries of the equation under study. We obtain the largest solvable Lie algebra. We also obtain the symmetry algebra and make a group classification of this equation. Further, some exact solutions are deduced and represented graphically.

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来源期刊

JOURNAL OF INTERDISCIPLINARY MATHEMATICS MATHEMATICS-

CiteScore

2.70

自引率

23.50%

发文量

141

期刊介绍： The Journal of Interdisciplinary Mathematics (JIM) is a world leading journal publishing high quality, rigorously peer-reviewed original research in mathematical applications to different disciplines, and to the methodological and theoretical role of mathematics in underpinning all scientific disciplines. The scope is intentionally broad, but papers must make a novel contribution to the fields covered in order to be considered for publication. Topics include, but are not limited, to the following: • Interface of Mathematics with other Disciplines • Theoretical Role of Mathematics • Methodological Role of Mathematics • Interface of Statistics with other Disciplines • Cognitive Sciences • Applications of Mathematics • Industrial Mathematics • Dynamical Systems • Mathematical Biology • Fuzzy Mathematics The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Editor-in-Chief’s discretion. Special issue proposals in cutting-edge and timely areas of research in interdisciplinary mathematical research are encouraged – please contact the Editor-in-Chief in the first instance.