Algebro-geometric finite gap solutions to the Korteweg-de Vries equation as primitive solutions

PHYSICA D-NONLINEAR PHENOMENA

卷:414

Article

Nabelek, Patrik, V¹ 

[1] Oregon State Univ, Dept Math, Kidder Hall 368, Corvallis, OR 97331 USA

关键词: The Korteweg-de Vries equation;    Finite gap potentials and solutions;    Primitive potentials and solutions;    Multi-soliton solutions;   

DOI  :  10.1016/j.physd.2020.132709

来源: Elsevier

【 摘 要 】

In this paper we show that all algebro-geometric finite gap solutions to the Korteweg-de Vries equation can be realized as a limit of N-soliton solutions as N diverges to infinity (see remark 1 for the precise meaning of this statement). This is done using the primitive solution framework initiated by Dyachenko et al. (2016) and Zakharov et al. (2016) [25, 26]. One implication of this result is that the N-soliton solutions can approximate any bounded periodic solution to the Korteweg-de Vries equation arbitrarily well in the limit as N diverges to infinity. We also study primitive solutions numerically that have the same spectral properties as the algebro-geometric finite gap solutions but are not algebro-geometric solutions. (c) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free