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The defocusing NLS equation : quasi-rational and rational solutions

2022

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.