Open AccessMultiparametric 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) , degree (music) , mathematics , polynomial , plane (geometry) , mathematical analysis , modulus , polynomial and rational function modeling , pure 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.