高阶Korteweg-de Vries方程组的存在性

IF 1 4区数学 Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-04-02 DOI:10.4236/AM.2021.124021

Min Liu

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引用次数: 0

摘要

考虑如下Korteweg-de Vries耦合方程组，其中u, v≥N≤7，λi，β > 0， β为实耦合参数。首先，利用Nehari流形上的变分法和最小化技术证明了一类Korteweg-de Vries方程耦合系统解的存在性。然后，我们利用分叉理论证明了方程的多重性，这在研究高阶方程时是很少见的。

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Existence for a Higher Order Coupled System of Korteweg-de Vries Equations

Consider the following system of coupled Korteweg-de Vries equations, where u, v ⊆ W2,2, 2≤N≤7 and λi,β > 0, β denotes a real coupling parameter. Firstly, we prove the existence of the solutions of a coupled system of Korteweg-de Vries equations using variation approach and minimization techniques on Nehari manifold. Then, we show the multiplicity of the equations by a bifurcation theory which is rare for studying higher order equations.

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来源期刊

Applied Mathematics-A Journal of Chinese Universities Series B MATHEMATICS, APPLIED-

自引率

10.00%

发文量

期刊介绍： Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects. The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry. Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.