Constructing new nonlinear evolution equations with supersymmetry

Rosie Hayward, Fabio Biancalana

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


The factorisation method commonly used in linear supersymmetric quantum mechanics is extended, such that it can be applied to nonlinear quantum mechanical systems. The new method is distinguishable from the linear formalism, as the superpotential is forced to become eigenfunction-dependent. Example solutions are given for the nonlinear Schrödinger equation and its supersymmetric partner equation. This method allows new nonlinear evolution equations to be constructed from the solutions of known nonlinear equations, and has the potential to be a useful tool for mathematicians and physicists working in the field of nonlinear systems, allowing the discovery of previously unknown 'dualities' amongst nonlinear evolution equations.

Original languageEnglish
Article number275202
JournalJournal of Physics A: Mathematical and Theoretical
Issue number27
Publication statusPublished - 4 Jun 2018


  • nonlinear evolution equations
  • nonlinear Schrödinger equation
  • solitons
  • supersymmetry

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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