Open AccessMulti-parametric Rational Solutions to the KdV Equation
Author(s) -
Pierre Gaillard
Publication year - 2021
Publication title -
asian journal of research and reviews in physics
Language(s) - English
Resource type - Journals
ISSN - 2582-5992
DOI - 10.9734/ajr2p/2021/v4i330143
Subject(s) - korteweg–de vries equation , degenerate energy levels , quotient , limit (mathematics) , mathematics , rational function , exponential function , parametric statistics , parametric equation , pure mathematics , mathematical analysis , physics , nonlinear system , quantum mechanics , statistics , geometry
We construct multi-parametric rational solutions to the KdV equation. For this, we use solutions in terms of exponentials depending on several parameters and take a limit when one of these parameters goes to 0. Here we present degenerate rational solutions and give a result without the presence of a limit as a quotient of polynomials depending on 3N parameters. We give the explicit expressions of some of these rational solutions.