The KP Approximation Under a Weak Coriolis Forcing
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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The Author declares that they have no competing interests or any potential conflict of interest.
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