6533b855fe1ef96bd12affaf
RESEARCH PRODUCT
Rational solutions to the KPI equation and multi rogue waves
Pierre Gaillardsubject
Physics[PHYS]Physics [physics]Pure mathematics[ PHYS ] Physics [physics]Hierarchy (mathematics)Plane (geometry)Rogue wavesRational solutions[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]General Physics and Astronomy01 natural sciences010305 fluids & plasmasKPI equationInteger[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesRogue wave010306 general physicsQuotientdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-04-01 |