Rational solutions to the KPI equation of order 7 depending on 12 parameters

Pierre Gaillard (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We construct in this paper, rational solutions as a quotient of two determinants of order 2N = 14 and we obtain what we call solutions of order N = 7 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 112 in x, y and t depending on 12 parameters. The maximum of modulus of these solutions at order 7 is equal to 2(2N + 1) 2 = 450. We make the study of the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6. When all these parameters grow, triangle and ring structures are obtained.

Mots clés: KPI equation; Fredholm determinants; Wronskians; rogue waves; lumps

Domaines: Physique mathématique [math-ph]

Pierre Gaillard. Rational solutions to the KPI equation of order 7 depending on 12 parameters. 2018. ⟨hal-01736228⟩