Rational solutions to the KPI equation and multi rogue waves

Abstract 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 2 N ( N + 1 ) in x , y and t depending on 2 N − 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.

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