- Journal of Mathematical Sciences and Modelling
- Vol: 5 Issue: 1
- Quasi-Rational and Rational Solutions to the Defocusing Nonlinear Schrödinger Equation
Quasi-Rational and Rational Solutions to the Defocusing Nonlinear Schrödinger Equation
Authors : Pierre Gaillard
Pages : 24-34
Doi:10.33187/jmsm.990955
View : 19 | Download : 10
Publication Date : 2022-04-30
Article Type : Research
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