Asymptotic stability of high-dimensional Zakharov-Kuznetsov solitons

DOI10.1007/s00205-015-0939-xzbMath1334.35276arXiv1406.3196OpenAlexW2150554298MaRDI QIDQ266895

Didier Pilod, Gideon Simpson, Raphaël Côte, Claudio Muñoz

Publication date: 7 April 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.3196

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear elliptic equations (35J60) Soliton equations (35Q51) Soliton solutions (35C08)

Related Items (31)

Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes ⋮ Nonlinear dynamics of a dispersive anisotropic Kuramoto–Sivashinsky equation in two space dimensions ⋮ Asymptotic stability of Zakharov-Kuznetsov solitons ⋮ On special regularity properties of solutions of the Zakharov-Kuznetsov equation ⋮ On the stability of the solitary waves to the (generalized) Kawahara equation ⋮ Orbital stability of a sum of solitons and breathers of the modified Korteweg–de Vries equation ⋮ Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher ⋮ On Kato's smoothing effect for a fractional version of the Zakharov-Kuznetsov equation ⋮ Higher dimensional generalization of the Benjamin‐Ono equation: 2D case ⋮ A determination of the blowup solutions to the focusing NLS with mass equal to the mass of the soliton ⋮ The existence of weak solutions and propagation regularity for a generalized KdV system ⋮ Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation ⋮ Numerical study of the transverse stability of line solitons of the Zakharov-Kuznetsov equations ⋮ Local well-posedness and spatial analyticity for the generalized Zakharov-Kuznetsov equation ⋮ Asymptotic stability manifolds for solitons in the generalized good Boussinesq equation ⋮ Instability of Solitons in the 2d Cubic Zakharov-Kuznetsov Equation ⋮ Solitons in the presence of a small, slowly varying perturbation ⋮ Normal form for transverse instability of the line soliton with a nearly critical speed of propagation ⋮ Stability for line solitary waves of Zakharov-Kuznetsov equation ⋮ On orbital instability of spectrally stable vortices of the NLS in the plane ⋮ On local energy decay for large solutions of the Zakharov-Kuznetsov equation ⋮ Numerical study of Zakharov-Kuznetsov equations in two dimensions ⋮ Center stable manifolds around line solitary waves of the Zakharov-Kuznetsov equation with critical speed ⋮ A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models ⋮ On asymptotic stability of nonlinear waves ⋮ The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space ⋮ Instability of solitons–revisited, II: The supercritical Zakharov-Kuznetsov equation ⋮ Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation ⋮ Stability of the solitary manifold of the perturbed sine-Gordon equation ⋮ Asymptotic 𝐾-soliton-like solutions of the Zakharov-Kuznetsov type equations ⋮ The Cauchy problem for the L²–critical generalized Zakharov-Kuznetsov equation in dimension 3

Cites Work

• Unnamed Item
• Unnamed Item
• The Fourier restriction norm method for the Zakharov-Kuznetsov equation
• From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov
• On uniqueness properties of solutions of the Zakharov-Kuznetsov equation
• A note on the Cauchy problem for the 2D generalized Zakharov-Kuznetsov equations
• A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results
• Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation
• Local and global well-posedness for the 2D generalized Zakharov-Kuznetsov equation
• On the support of solutions to the Zakharov-Kuznetsov equation
• On asymptotic stability of kink for relativistic Ginzburg-Landau equations
• A remark on the modified Zakharov-Kuznetsov equation in three space dimensions
• Nonlinear scalar field equations. I: Existence of a ground state
• The Toda system and multiple-end solutions of autonomous planar elliptic problems
• Construction of solutions to the \(L^2\)-critical KdV equation with a given asymptotic behaviour
• The Cauchy problem for the 3D Zakharov-Kuznetsov equation
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
• Asymptotic stability of solitary waves
• Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
• Stability and asymptotic stability for subcritical gKdV equations
• A note on the unique continuation property for Zakharov--Kuznetsov equation
• Bilinear Strichartz estimates for the Zakharov-Kuznetsov equation and applications
• Asymptotic stability of solitons of the gKdV equations with general nonlinearity
• Proof of a spectral property related to the singularity formation for the \(L^{2}\) critical nonlinear Schrödinger equation
• Asymptotic stability of solitons for the Benjamin-Ono equation
• Large Time Asymptotics of Solutions Around Solitary Waves to the Generalized Korteweg--de Vries Equations
• Restriction for homogeneous polynomial surfaces in $\mathbb {R}^3$
• The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation
• Vortex collapse for the L2-critical nonlinear Schrödinger equation
• Asymptotic stability of the black soliton for the Gross–Pitaevskii equation
• Kink dynamics in the $\phi ^4$ model: Asymptotic stability for odd perturbations in the energy space
• Spectral analysis for matrix Hamiltonian operators
• Smoothness and Exponential Decay ofL²-Compact Solutions of the Generalized KdV Equations
• Well-Posedness Results for the Three-Dimensional Zakharov--Kuznetsov Equation
• Linear Problems Related to Asymptotic Stability of Solitons of the Generalized KdV Equations
• Well-Posedness for the Two-Dimensional Modified Zakharov–Kuznetsov Equation
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Asymptotic stability of solitons of the subcritical gKdV equations revisited
• Stability and instability of some nonlinear dispersive solitary waves in higher dimension
• The Gardner equation and the 𝐿²-stability of the 𝑁-soliton solution of the Korteweg-de Vries equation
• $L^2$-stability of solitary waves for the KdV equation via Pego and Weinstein's method
• Embedded eigenvalues and the nonlinear Schrödinger equation
• Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension
• Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation
• Instability of solitons for the critical generalized Korteweg-de Vries equation
• Asymptotic stability of solitons for subcritical generalized KdV equations

This page was built for publication: Asymptotic stability of high-dimensional Zakharov-Kuznetsov solitons