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

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.