N-order solutions to the Gardner equation in terms of Wronskians

Authors : Pierre Gaillard

Pages : 75-81

Doi:10.33187/jmsm.1426590

View : 52 | Download : 90

Publication Date : 2024-08-31

Article Type : Research Paper

Abstract :$N$-order solutions to the Gardner equation (G) are given in terms of Wronskians of order $N$ depending on $2N$ real parameters. We get solutions expressed with trigonometric or hyperbolic functions. When one of the parameters goes to $0$, we succeed to get for each positive integer $N$, rational solutions as a quotient of polynomials in $x$ and $t$ depending on $2N$ real parameters. We construct explicit expressions of these rational solutions for the first orders.
Keywords : Gardner equation, Rational Solutions, Wronskians