Journal
ANNALS OF PHYSICS
Volume 367, Issue -, Pages 1-5Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2016.01.013
Keywords
KPI equation; Rational solutions; Rogue waves
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We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, y and t depending on 2N - 2 real parameters for each positive integer N. We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x, y) plane for different values of time t and parameters. (C) 2016 Elsevier Inc. All rights reserved.
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