Multiparametric Rational Solutions of Order N to the KPI Equation and the Explicit Case of Order 3 | Zendy

Pierre Gaillard | Zendy

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Multiparametric Rational Solutions of Order N to the KPI Equation and the Explicit Case of Order 3

Author(s) -

Pierre Gaillard

Publication year - 2021

Publication title -

archives of current research international

Language(s) - English

Resource type - Journals

ISSN - 2454-7077

DOI - 10.9734/acri/2021/v21i630253

Subject(s) - quotient , order (exchange) , mathematics , degree (music) , polynomial , plane (geometry) , polynomial and rational function modeling , modulus , mathematical analysis , pure mathematics , combinatorics , discrete mathematics , geometry , physics , finance , acoustics , economics

We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed as a quotient of a polynomial of degree 2N(N +1)−2 in x, y and t by a polynomial of degree 2N(N +1) in x, y and t, depending on 2N − 2 real parameters. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.

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