From first to fourth order rational solutions to the Boussinesq equation

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in x and t. For each positive integer N , the numerator is a polynomial of degree N (N + 1) − 2 in x and t, while the denominator is a polynomial of degree N (N + 1) in x and t. So we obtain a hierarchy of rational solutions depending on an integer N called the order of the solution. We construct explicit expressions of these rational solutions for N = 1 to 4.

Mots clés: Boussinesq equation; rational solutions; rogue waves PACS numbers : 33Q55; 37K10; 4710A-; 4735Fg; 4754Bd

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. From first to fourth order rational solutions to the Boussinesq equation. 2020. ⟨hal-02500568⟩