Symmetries and reductions of integrable nonlocal partial differential equations

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article number884
JournalSymmetry
Volume11
Issue number7
DOIs
Publication statusPublished - 2019 Jul 1

Fingerprint

Korteweg-de Vries equation
Nonlocal Equations
partial differential equations
Partial differential equations
Differential equations
Partial differential equation
Symmetry
Difference equations
symmetry
Modified Equations
Korteweg-de Vries Equation
Nonlinear equations
Ordinary differential equations
differential equations
Differential equation
Lie Point Symmetries
Differential-difference Equations
Integrable Equation
Nonlinear Equations
Ordinary differential equation

Keywords

  • Continuous symmetry
  • Integrable nonlocal partial differential equations
  • Symmetry reduction

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

Cite this

Symmetries and reductions of integrable nonlocal partial differential equations. / Peng, Linyu.

In: Symmetry, Vol. 11, No. 7, 884, 01.07.2019.

Research output: Contribution to journalArticle

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