Multi-parametric Rational Solutions to the KdV Equation
Pierre Gaillard *
Institut de Mathematiques de Bourgogne Franche Comt ´ e, Universit ´ e de Bourgogne, 9 Avenue Alain ´ Savary BP 47870 21078 Dijon Cedex, France.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: KdV equation, rational solutions