Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 3, pp 1229–1247 | Cite as

The KP Approximation Under a Weak Coriolis Forcing

  • Benjamin Melinand


In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq–Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev–Petviashvili equation (also called Grimshaw–Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev–Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.


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The author would like to thank Jean-Claude Saut for the fruitful discussions about the KP approximation.

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Conflict of interest

The Author declares that they have no competing interests or any potential conflict of interest.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Indiana UniversityIndianapolisUSA

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