Nondegeneracy, Morse index and orbital stability of the KP-I lump solution
From MaRDI portal
Publication:2326460
DOI10.1007/s00205-019-01413-5zbMath1428.35458OpenAlexW2957025154MaRDI QIDQ2326460
Publication date: 7 October 2019
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00205-019-01413-5
Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Spectral theory and eigenvalue problems for partial differential equations (35P99) Index theory for dynamical systems, Morse-Conley indices (37B30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Traveling wave solutions (35C07) Soliton solutions (35C08)
Related Items (6)
Fully localised three-dimensional gravity-capillary solitary waves on water of infinite depth ⋮ Traveling water waves — the ebb and flow of two centuries ⋮ Smooth branch of rarefaction pulses for the nonlinear Schrödinger equation and the Euler-Korteweg system in 2d ⋮ Linear stability of elastic 2-line solitons for the KP-II equation ⋮ On asymptotic stability of nonlinear waves ⋮ Instability and blow-up of solutions of the fifth-order KP equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
- Stability and instability of the KdV solitary wave under the KP-I flow
- Description of two soliton collision for the quartic gKdV equation
- Stability of the line soliton of the KP-II equation under periodic transverse perturbations
- 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
- Stability theory of solitary waves in the presence of symmetry. II
- Global well-posedness of the KP-I initial-value problem in the energy space
- The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
- Transverse nonlinear instability for two-dimensional dispersive models
- Stability theory of solitary waves in the presence of symmetry. I
- Bäcklund transformations and their applications
- On the Cauchy problem for the Kadomtsev-Petviashvili equation
- Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation
- 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
- The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
- A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili I equations
- Global well-posedness of partially periodic KP-I equation in the energy space and application
- Remark on the semilinear ill-posedness for a periodic higher-order KP-I equation
- On the local and global well-posedness theory for the KP-I equation
- Global well-posedness for the KP-I equation
- Recent results on the generalized Kadomtsev-Petviashvili equations
- Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations
- Asymptotic stability of \(N\)-solitary waves of the FPU lattices
- On the transverse instability of solitary waves in the Kadomtsev-Petviashvili equation
- On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation
- Stability of the line soliton of the Kadomtsev-Petviashvili-I equation with the critical traveling speed.
- Lump solutions to the Kadomtsev-Petviashvili equation
- Interaction of two lump solitons described by the Kadomtsev-Petviashvili equation
- Rarefaction pulses for the nonlinear Schrödinger equation in the transonic limit
- Global well-posedness for the KP-I equation on the background of a non-localized solution
- Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's
- Travelling waves for the Gross-Pitaevskii equation. II
- Backlund Transformation and L2-stability of NLS Solitons
- Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg—de Vries equation
- Asymptotic stability of Toda lattice solitons
- Stability and instability of solitary waves of Korteweg-de Vries type
- Two-dimensional lumps in nonlinear dispersive systems
- Decay mode solution of the two-dimensional KdV equation and the generalized Bäcklund transformation
- Rational solutions of integrable equations via nonlinear superposition formulae
- Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution
- Symmetries and Decay of the Generalized Kadomtsev--Petviashvili Solitary Waves
- Blow up and instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation
- Multiple branches of travelling waves for the Gross–Pitaevskii equation
- Motions in a Bose condensate: X. New results on the stability of axisymmetric solitary waves of the Gross–Pitaevskii equation
- Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions
- Phase dynamics of periodic waves leading to the Kadomtsev–Petviashvili equation in 3+1 dimensions
- Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity
This page was built for publication: Nondegeneracy, Morse index and orbital stability of the KP-I lump solution
