Paper

Long time asymptotics of large data in the Kadomtsev–Petviashvili models

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Published 2 April 2024 • © 2024 IOP Publishing Ltd & London Mathematical Society
, , Citation Argenis J Mendez et al 2024 Nonlinearity 37 055017 DOI 10.1088/1361-6544/ad359e

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Author e-mails

amendez@dim.uchile.cl

cmunoz@dim.uchile.cl

felipe.poblete@uach.cl

jpozo@uchile.cl

Author affiliations

1 Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile

2 CNRS and Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (AFB170001 and UMI 2807 CNRS), Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile

3 Instituto de Ciencias Físicas y Matemáticas, Facultad de Ciencias, Universidad Austral de Chile, Valdivia, Chile

4 Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Santiago, Chile

Author notes

5 This work was partially supported by CMM Conicyt Proyecto Basal AFB170001 and by Postdoc FONDECYT Project 3210727.

6 C M's work was funded in part by Chilean research Grants Exploration Project 13220060, FONDECYT 1191412, 1231250 and Centro de Modelamiento Matemático (CMM), ACE210010 and FB210005, BASAL funds for centers of excellence from ANID-Chile, Project France–Chile ECOS-Sud C18E06, MathAmSud EEQUADD II, MathAmSud WAFFLE 23-MATH-18 and CMM ANID PIA AFB170001.

7 F P's work is partially supported by ANID Exploration Project 13220060, ANID Project FONDECYT 1221076 and MathAmSud WAFFLE 23-MATH-18

8 J C P's work was partially supported by Chilean research Grants Exploration Project 13220060 and FONDECYT 1221271.

9 Author to whom any correspondence should be addressed.

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Dates

  1. Received 30 May 2023
  2. Accepted 19 March 2024
  3. Published

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0951-7715/37/5/055017

Abstract

We consider the Kadomtsev–Petviashvili (KP) equations posed on $\mathbb{R}^2$. For both models, we provide sequential in time asymptotic descriptions of solutions obtained from arbitrarily large initial data, inside regions of the plane 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. This new approach is particularly important in the KP-I case, where no monotonicity property was previously known. The core of our results do not require the use of the integrability of KP and are adaptable to well-posed perturbations.

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10.1088/1361-6544/ad359e