库珀什密特超级 KdV 方程的双哈密顿结构

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-08-17 DOI:10.1016/j.aml.2024.109280

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引用次数: 0

摘要

本文研究了 Kupershmidt 提出的超级 Korteweg-de Vries（sKdV）方程，该方程拥有一个包含三个完全非局部项的 Lax 算子。我们对拉克斯算子进行了重新表述，使其成为超约束修正卡多姆采夫-彼得维亚什维利（scmKP）类型。通过计算 scmKP 层次的双哈密顿结构并采用狄拉克还原法，我们得到了 sKdV 方程的双哈密顿结构。我们还提出了其修正系统的谱问题。

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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Bi-Hamiltonian structure of a super KdV equation of Kupershmidt

In this paper, we study a super Korteweg–de Vries (sKdV) equation proposed by Kupershmidt which possesses a Lax operator with three fully nonlocal terms. The Lax operator is reformulated so that it is of the super constrained modified Kadomtsev–Petviashvili (scmKP) type. By calculating the bi-Hamiltonian structure of the scmKP hierarchy and employing Dirac reduction, we obtain the bi-Hamiltonian structure of the sKdV equation. We also present a spectral problem of its modified system.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.