Uniqueness of lump solution to the KP-I equation

KdV equations (Korteweg-de Vries equations) (35Q53) Initial value problems for nonlinear higher-order PDEs (35G25) Traveling wave solutions (35C07) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

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On the KPI transonic limit of two-dimensional Gross-Pitaevskii travelling waves
Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation
The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
Rational solutions of the Zakharov-Shabat equations and completely integrable systems of \(N\) particles on a line
On a class of polynomials connected with the Korteweg-de Vries equation
Rational solutions of the Kadomtsev-Petviashvili equation and integrable systems of \(n\) particles on a line
The structure of the rational solutions to the Boussinesq equation
The Boussinesq equation revisited
Solitary waves of generalized Kadomtsev-Petviashvili equations
Nonlinear stability of solitary waves of a generalized Kadomtsev-Petviashvili equation
Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili I equations
On the local and global well-posedness theory for the KP-I equation
Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions
Solutions of the Boussinesq equation
On additional symmetry: The many-body problem related to the KP hierarchy
On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation
Nonlinear dispersive equations. Inverse scattering and PDE methods
Nondegeneracy, Morse index and orbital stability of the KP-I lump solution
Global well-posedness for the KP-I equation on the background of a non-localized solution
Multi-lump wave patterns of KPI via integer partitions
IST Versus PDE: A Comparative Study
Direct and inverse scattering transforms with arbitrary spectral singularities
On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
Direct and inverse scattering on the line with arbitrary singularities
Rational solutions of the classical Boussinesq hierarchy
Scattering and inverse scattering for first order systems
Scattering and inverse scattering for first-order systems: II
Two-dimensional lumps in nonlinear dispersive systems
Inverse scattering and the boussinesq equation
Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem
A New Approach to the Boussinesq Hierarchy
Solutions of the KPI equation with smooth initial data
Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution
Calogero–Moser hierarchy and KP hierarchy
Symmetries and Decay of the Generalized Kadomtsev--Petviashvili Solitary Waves
Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions
The Riemann–Hilbert Problem and Inverse Scattering
Classification of KPI lumps
The "good" Boussinesq equation: a Riemann-Hilbert approach
A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
Lump Solutions for PDE's: Algorithmic Construction and Classification
RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION
The ``good Boussinesq equation: long-time asymptotics

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