Journal of Basic and Applied Research International

6-TH ORDER RATIONAL SOLUTIONS TO THE KPI EQUATION DEPENDING ON 10 PARAMETERS

PIERRE GAILLARD *

Institut de Mathematiques de Bourgogne, Universite de Bourgogne, 9 avenue Alain Savary BP 47870, 21078 Dijon Cedex, France.

*Author to whom correspondence should be addressed.

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Abstract

Here 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.

Keywords: KP equation, Fredholm determinants, Wronskians, rogue waves, lumps

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