Non-holonomic and quasi-integrable deformations of the AB equations

Kumar Abhinav, Indranil Mukherjee, Partha Guha

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

For the first time both non-holonomic and quasi-integrable deformations are obtained for the AB system of coupled equations. The AB system models geophysical and atmospheric fluid motion along with ultra-short pulse propagation in nonlinear optics, and serves as a generalization of the well-known sine-Gordon equation. The non-holonomic deformation retains integrability subjected to higher-order differential constraints whereas the quasi-AB system, which is partially deviated from integrability, is characterized by an infinite subset of quantities (charges) that are conserved only asymptotically given the solution possesses definite space–time parity properties. Particular localized solutions to both these deformations of the AB system are obtained, some of which are qualitatively unique to the corresponding deformation, displaying similarities with physically observed excitations.

Original languageBritish English
Article number133186
JournalPhysica D: Nonlinear Phenomena
Volume433
DOIs
StatePublished - May 2022

Keywords

  • AB equations
  • Nonholonomic deformations
  • Quasi-integrable deformations

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