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Special polynomials associated with rational solutions of the defocusing nonlinear Schrödinger equation and the fourth Painlevé equation

Published online by Cambridge University Press:  13 June 2006

PETER A. CLARKSON
PETER A. CLARKSON
Affiliation:
Institute of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury CT2 7NF, UK Email: [email protected]
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Abstract

Rational solutions and rational-oscillatory solutions of the defocusing nonlinear Schrödinger equation are expressed in terms of special polynomials associated with rational solutions of the fourth Painlevé equation. The roots of these special polynomials have a regular, symmetric structure in the complex plane. The rational solutions verify results of Nakamura and Hirota [J. Phys. Soc. Japan, 54 (1985) 491–499] whilst the rational-oscillatory solutions appear to be new solutions of the defocusing nonlinear Schrödinger equation.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 17 , Issue 3 , June 2006 , pp. 293 - 322
Copyright
2006 Cambridge University Press

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