Stability of Kadomtsev-Petviashvili multi-line solitons

Stability in context of PDEs (35B35) Scattering theory for PDEs (35P25) Integral representations of solutions to PDEs (35C15) Soliton equations (35Q51) Initial value problems for nonlinear higher-order PDEs (35G25) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Soliton solutions (35C08)

Cites Work

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Extended resolvent of the heat operator with a multisoliton potential
Stability and instability of the KdV solitary wave under the KP-I flow
Global well-posedness for the KP-II equation on the background of a non-localized solution
Stability of the line soliton of the KP-II equation under periodic transverse perturbations
Transverse nonlinear instability for two-dimensional dispersive models
Building an extended resolvent of the heat operator via twisting transformations
Inverse scattering for the heat operator and evolutions in \(2+1\) variables
Two-dimensional ``inverse scattering problem for negative energies and generalized-analytic functions. I: Energies below the ground state
Hamiltonian structure of the Kadomtsev-Petviashvili. II: Equation in the class of decreasing Cauchy data
Nonsingularity of the direct scattering transform for the KP II equation with a real exponentially decaying-at-infinity potential
Stability and asymptotic stability for subcritical gKdV equations
Nonlinear dispersive equations. Inverse scattering and PDE methods
Orbital stability of KdV multisolitons in \(H^{-1}\)
The equivalence of different approaches for generating multisoliton solutions of the KPII equation
The Deodhar decomposition of the Grassmannian and the regularity of KP solitons
Global well-posedness for the KP-I equation on the background of a non-localized solution
Towards an inverse scattering theory for non-decaying potentials of the heat equation
Stability of line solitons for the KP-II equation in ℝ²
KP Solitons and the Grassmannians
IST of KPII equation for perturbed multisoliton solutions
On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
Soliton solutions of the Kadomtsev-Petviashvili II equation
Soliton Solutions of the KP Equation and Application to Shallow Water Waves
Lyapunov stability of ground states of nonlinear dispersive evolution equations
On the stability theory of solitary waves
On the stability of KdV multi‐solitons
On a family of solutions of the Kadomtsev–Petviashvili equation which also satisfy the Toda lattice hierarchy
On some nondecaying potentials and related Jost solutions for the heat conduction equation
Asymptotic stability of solitons of the subcritical gKdV equations revisited
On the initial value problem for the KPII equation with data that do not decay along a line
Inverse scattering theory of the heat equation for a perturbed one-soliton potential
The Gardner equation and the 𝐿²-stability of the 𝑁-soliton solution of the Korteweg-de Vries equation
The Phase Shift of Line Solitons for the KP-II Equation
Solitons in Two-Dimensional Shallow Water
The direct scattering problem for the perturbed Gr(1, 2)_⩾0 Kadomtsev–Petviash-vili II solitons
The direct scattering problem for perturbed Kadomtsev–Petviashvili multi line solitons

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