Rational solutions to the Johnson equation of order N depending on 2N − 2 parameters

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We construct rational solutions of order N depending on 2N − 2 parameters. They can be written as a quotient of 2 polynomials of degree 2N (N + 1) in x, t and 4N (N + 1) in y depending on 2N − 2 parameters. We explicitly construct the expressions of the rational solutions of order 4 depending on 6 real parameters and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, b1, b2, b3.

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Rational solutions to the Johnson equation of order N depending on 2N − 2 parameters. 2019. ⟨hal-02111571⟩