Quasi-Rational and Rational Solutions to the Defocusing Nonlinear Schr¨odinger Equation

Abstract

Quasi-rational solutions to the defocusing nonlinear Schr¨odinger 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.