On modulated coupled systems. Canonical reduction via reciprocal transformations

Colin Rogers, Wolfgang K. Schief*, Boris Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


It is shown how classes of modulated coupled systems of sine-Gordon, Demoulin and Manakov-type may be reduced to their unmodulated counterparts via the application of a novel reciprocal transformation. Modulations governed by recently introduced integrable Ermakov-Painlevé II, Ermakov-Painlevé III and Ermakov-Painlevé IV equations as well as the classical Ermakov equation are considered. In the latter case, the procedure is illustrated by the generation of a class of exact solutions to a heterogeneous Manakov system with periodic modulation.

Original languageEnglish
Article number105091
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - Apr 2020


  • Heterogeneous integrable system
  • Manakov system
  • Modulated soliton
  • Reciprocal transformation


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