Self-similar solutions of certain coupled integrable systems

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Published 22 January 2003 • Published under licence by IOP Publishing Ltd
, , Citation S Chakravarty et al 2003 J. Phys. A: Math. Gen. 36 1371 DOI 10.1088/0305-4470/36/5/313

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Author affiliations

1 Department of Mathematics, University of Colorado, Colorado Springs, CO 80933-7150, USA

2 Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK

3 Department of Mathematics and Statistics, Youngstown State University, Youngstown, OH 44555, USA

Dates

  1. Received 2 September 2002
  2. Published

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0305-4470/36/5/1371

Abstract

Similarity reductions of the coupled nonlinear Schrödinger equation and an integrable version of the coupled Maxwell–Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painlevé transcendents, leading to new exact self-similar solutions for these integrable equations.

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