6-th order rational solutions to the KPI equation depending on 10 parameters

International audienceHere we constuct rational solutions of order 6 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 84 in x, y and t depending on 10 parameters. We verify that the maximum of modulus of these solutions at order 6 is equal to 2(2N + 1)2 = 338. We study the patterns of their modulus in the plane (x, y) and their evolution according time and parameters a1, a2, a3, a4, a5, b1, b2, b3, b4, b5. When these parameters grow, triangle and rings structures are obtained