2024/05/12 by Alegría, Francisco, Chen, Gong, Muñoz, Claudio +2
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2405.07125
We consider the Kadomtsev-Petviashvili II (KP) model placed in \mathbb Rt × \mathbb Rx,y2, in the case of smooth data that are not necessarily in a Sobolev space. In this paper, the subclass of smooth solutions we study is of ``soliton type'', characterized by a phase Θ=Θ(t,x,y) and a unidimensional profile F. In particular, every classical KP soliton and multi-soliton falls into this category with suitable Θ and F. We establish concrete characterizations of KP solitons by means of a natural set of nonlinear differential equations and inclusions of functionals of Wronskian, Airy and Heat types, among others. These functional equations only depend on the new variables Θ and F. A distinct characteristic of this set of functionals is its special and rigid structure tailored to the considered soliton. By analyzing Θ and F, we establish the uniqueness of line-solitons, multi-solitons, and other degenerate solutions among a large class of KP solutions. Our results are also valid for other 2D dispersive models such as the quadratic and cubic Zakharov-Kuznetsov equations.