Journal of Mathematical Sciences and Modelling (Apr 2022)

Quasi-Rational and Rational Solutions to the Defocusing Nonlinear Schrödinger Equation

  • Pierre Gaillard

DOI
https://doi.org/10.33187/jmsm.990955
Journal volume & issue
Vol. 5, no. 1
pp. 24 – 34

Abstract

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Quasi-rational solutions to the defocusing nonlinear Schrödinger equation (dNLS) in terms of wronskians and Fredholm determinants of order $2N$ depending on $2N-2$ real parameters are given. We get families of quasi-rational solutions to the dNLS equation expressed as a quotient of two polynomials of degree $N(N+1)$ in the variables $x$ and $t$. We present also rational solutions as a quotient of determinants involving certain particular polynomials.

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