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 |
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論文番号 | 884 |
ジャーナル | Symmetry |
巻 | 11 |
号 | 7 |
DOI | |
出版ステータス | Published - 2019 7月 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)