Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System

  title={Ermakov-Painlev{\'e} II Symmetry Reduction of a Korteweg Capillarity System},
  author={Colin Rogers and Peter A. Clarkson},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  • C. Rogers, P. A. Clarkson
  • Published 2017
  • Mathematics, Physics
  • Symmetry Integrability and Geometry-methods and Applications
A class of nonlinear Schr\"{o}dinger equations involving a triad of power law terms together with a de Broglie-Bohm potential is shown to admit symmetry reduction to a hybrid Ermakov-Painlev\'{e} II equation which is linked, in turn, to the integrable Painlev\'{e} XXXIV equation. A nonlinear Schr\"{o}dinger encapsulation of a Korteweg-type capillary system is thereby used in the isolation of such a Ermakov-Painlev\'{e} II reduction valid for a multi-parameter class of free energy functions… Expand
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