复值KdV方程的第一个积分爆破解

IF 1.1 Q1 MATHEMATICS JOURNAL OF INTERDISCIPLINARY MATHEMATICS Pub Date : 2023-01-01 DOI:10.47974/jim-1511

B. Gwaxa, S. Jamal

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引用次数: 0

摘要

应用李理论确定了使复值Korteweg-de Vries方程保持不变的单参数点变换。构造了系统的守恒向量。我们提供行波约简，得到三阶常微分方程。这些方程是高度非线性的，不能直接求解，因此，我们建立了它们的第一个积分。后者是二阶的，有利于分析复值系统，以及一些有趣的爆破解。

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First integral blow-up solutions to complex-valued KdV equations

We apply Lie theory to determine the aone-parameter point transformations which leave complex-valued Korteweg-de Vries equations invariant. The conserved vectors of the systems are constructed. We provide travelling wave reductions that lead to third-order ordinary differential equations. These equations are highly nonlinear to solve directly and, therefore, we establish their first integrals. The latter is of second-order and facilitates the analysis of the complex-valued system, as well as some interesting blow-up solutions.

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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.