Soliton-like behaviour in non-integrable systems

Raghavendra Nimiwal, Urbashi Satpathi, Vishal Vasan, Manas Kulkarni

Research output: Contribution to journalArticlepeer-review


We present a general scheme for constructing robust excitations (soliton-like) in non-integrable multicomponent systems. By robust, we mean localised excitations that propagate with almost constant velocity and which interact cleanly with little to no radiation. We achieve this via a reduction of these complex systems to more familiar effective chiral field-theories using perturbation techniques and the Fredholm alternative. As a specific platform, we consider the generalised multicomponent nonlinear Schrödinger equations (MNLS) with arbitrary interaction coefficients. This non-integrable system reduces to uncoupled Korteweg-de Vries (KdV) equations, one for each sound speed of the system. This reduction then enables us to exploit the multi-soliton solutions of the KdV equation which in turn leads to the construction of soliton-like profiles for the original non-integrable system. We demonstrate that this powerful technique leads to the coherent evolution of excitations with minimal radiative loss in arbitrary non-integrable systems. These constructed coherent objects for non-integrable systems bear remarkably close resemblance to true solitons of integrable models. Although we use the ubiquitous MNLS system as a platform, our findings are a major step forward towards constructing excitations in generic continuum non-integrable systems.

Original languageEnglish
Article number425701
JournalJournal of Physics A: Mathematical and Theoretical
Issue number42
StatePublished - 22 Oct 2021
Externally publishedYes


  • Generalised multicomponent nonlinear Schrödinger equations
  • Integrablemodels,Korteweg-de Vries equation
  • Nonlinear dynamics
  • Solitons

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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