From KP-I lump solution to travelling waves of Gross-Pitaevskii equation

Liu, Yong; Wang, Zhengping; Wei, Juncheng; Yang, Wen Yong

doi:10.48550/arxiv.2110.15472

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, in [8](see also the references therein), it is shown that KP equation is related to the GP equation. The nondegeneracy result for the lump can then be used to construct traveling wave solutions of the GP equation with subsonic speed, with a perturbation argument; see [39].…”

Section: Introductionmentioning

confidence: 99%

Uniqueness of lump solution to the KP‐I equation

Liu,

Wei,

Yang

2024

Proceedings of London Math Soc

View full text Add to dashboard Cite

The KP‐I equation has family of solutions which decay to zero at space infinity. One of these solutions is the classical lump solution, which is a traveling wave, and the KP‐I equation in this case reduces to the Boussinesq equation. In this paper we classify all the ‘lump‐type’ solutions of the Boussinesq equation. Using a robust inverse scattering transform developed by Bilman–Miller for the Schrödinger equation, we show that the lump‐type solutions are rational and their functions have to be polynomials of degree for some integer . In particular, this implies that the lump solution is the unique ground state of the KP‐I equation (as conjectured by Klein–Saut). The problem studied in this paper was mentioned in Airault–McKean–Moser, our result can be regarded as a two‐dimensional analogy of their theorem on the classification of rational solutions for the KdV equation.

show abstract

Section: Introductionmentioning

confidence: 99%