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

Year 2022, Volume: 5 Issue: 1, 24 - 34, 30.04.2022

Pierre Gaillard

https://doi.org/10.33187/jmsm.990955

Abstract

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.

Keywords

defocusing NLS equation, polynomials, wronkians, Fredholm determinants

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