2021/01/22 by Mendez, Argenis J., Muñoz, Claudio, Poblete, Felipe +1 · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2101.08921
We consider the Kadomtsev-Petviashvili (KP) equations posed on ℝ2. For both equations, we provide sequential in time asymptotic descriptions of solutions, of arbitrarily large data, inside regions not containing lumps or line solitons, and under minimal regularity assumptions. The proof involves the introduction of two new virial identities adapted to the KP dynamics, showing decay in large regions of space, especially in the KP-I case, where no monotonicity property was previously known. Our results do not require the use of the integrability of KP and are adaptable to well-posed perturbations of KP.