退化拉克斯可积方程的新精确解和守恒律

Q1 Mathematics
Muhammad Alim Abdulwahhab
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引用次数: 0

摘要

利用李对称群这一通用而强大的方法,对退化的拉克斯可积方程进行了广泛的分析。证明了该可积方程具有无穷李代数,并将任意函数专门化为一阶多项式后,得到23个显式生成元,用于构造不同的非平凡不变解。本文还将建立三个独立的积分解,其被积函数包含绝对任意的不附加任何条件的函数。它们的任意性可用于生成所考虑的(2+1)维线性退化拉克斯可积方程(即巴甫洛夫方程)的非平凡和无限多个精确不变解的概要。这意味着在任何数学手册中报告的所有有效的积分解都可以使用适当的不变量作为巴甫洛夫方程的解。除了上述新颖的解外,还建立了三阶乘子,并将其用于构建低阶局部守恒律。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
New exact solutions and conservation laws of a degenerate Lax-integrable equation
This study uses the Lie symmetry group, a versatile and powerful method, to carry out an extensive analyses on a degenerate Lax-integrable equation. This integrable equation is shown to have infinite Lie algebra, and after specializing the arbitrary functions to first order polynomials, twenty-three explicit generators are obtained which are used to construct distinct non-trivial invariant solutions. This research article will also establish three independent integral solutions whose integrands contained functions that are absolutely arbitrary without any condition attached. Their arbitrariness can be used to generate compendium of nontrivial and infinitely many exact invariant solutions to the (2+1)-dimensional linearly degenerate Lax-integrable equation under consideration, which is known as the Pavlov equation. This means that all valid solutions of integrals reported in any mathematical handbooks can be adapted as solutions to the Pavlov equation using the appropriate invariants. Apart from the aforementioned novelty solutions, 3rd-order multipliers are also established and used to construct lower-order local conservation laws.
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来源期刊
CiteScore
6.20
自引率
0.00%
发文量
138
审稿时长
14 weeks
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