Symmetries and reductions of integrable nonlocal partial differential equations

Linyu Peng

研究成果: Article査読

抄録

In this paper, symmetry analysis is extended to study nonlocal differential equations. In particular, two integrable nonlocal equations are investigated, the nonlocal nonlinear Schrödinger equation and the nonlocal modified Korteweg-de Vries equation. Based on general theory, Lie point symmetries are obtained and used to reduce these equations to nonlocal and local ordinary differential equations, separately; namely, one symmetry may allow reductions to both nonlocal and local equations, depending on how the invariant variables are chosen. For the nonlocal modified Korteweg-de Vries equation, analogously to the local situation, all reduced local equations are integrable. We also define complex transformations to connect nonlocal differential equations and differential-difference equations.

本文言語English
論文番号884
ジャーナルSymmetry
11
7
DOI
出版ステータスPublished - 2019 7 1

ASJC Scopus subject areas

  • コンピュータ サイエンス(その他)
  • 化学(その他)
  • 数学 (全般)
  • 物理学および天文学(その他)

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