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

Authors : Pierre GAİLLARD

Pages : 24-34

Doi:10.33187/jmsm.990955

View : 12 | Download : 6

Publication Date : 2022-04-30

Article Type : Research Paper

Abstract :Quasi-rational solutions to the defocusing nonlinear Schrödinger equation insert ignore into journalissuearticles values(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 $Ninsert ignore into journalissuearticles values(N+1);$ 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