6533b81ffe1ef96bd12781df

RESEARCH PRODUCT

Solutions to the Gardner equation with multi-parameters and the rational case

Pierre Gaillard

subject

wronskiansrational solutionsGardner equation[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]

description

We construct solutions to the Gardner equation in terms of trigonometric and hyperbolic functions, depending on several real parameters. Using a passage to the limit when one of these parameters goes to 0, we get, for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 3. We easily deduce solutions to the mKdV equation in terms of wronskians as well as rational solutions depending on 2N real parameters.

https://hal.science/hal-03617682v2