Stability and asymptotic stability for subcritical gKdV equations

From MaRDI portal
Publication:1871679

DOI10.1007/s00220-002-0723-2zbMath1017.35098OpenAlexW1658726539MaRDI QIDQ1871679

Tai-Peng Tsai, Yvan Martel, Frank Merle

Publication date: 4 May 2003

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-002-0723-2




Related Items (only showing first 100 items - show all)

Logarithmic Schrödinger equations in infinite dimensionsOrbital stability of periodic peakons for a new higher-order μ-Camassa–Holm equationStrongly interacting solitary waves for the fractional modified Korteweg-de Vries equationAsymptotic \(N\)-soliton-like solutions of the fractional Korteweg-de Vries equationBlow-up solutions forL2supercritical gKdV equations with exactlykblow-up pointsAsymptotic Stability of KdV Solitons on the Half-Line: A Study in the Energy SpaceOn asymptotic stability of the sine-Gordon kink in the energy spaceDynamics of two interacting kinks for the \(\phi^6\) modelAsymptotic stability and classification of multi-solitons for Klein-Gordon equationsOrbital stability of two-component peakonsMultisolitons are the unique constrained minimizers of the KdV conserved quantitiesStability of periodic peakons for a nonlinear quartic \(\mu\)-Camassa-Holm equationOrbital stability of the sum of N solitary waves for the hyperelastic-rod wave equationWhy are solitons stable?Asymptotic 𝐾-soliton-like solutions of the Zakharov-Kuznetsov type equationsIsoinertial operators around the KdV multi-solitonsStability of the train of \(N\) solitary waves for the two-component Camassa-Holm shallow water systemAsymptotic stability of high-dimensional Zakharov-Kuznetsov solitonsStability of the Camassa-Holm multi-peakons in the dynamics of a shallow-water-type systemAsymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger EquationsInelasticity of soliton collisions for the 5D energy critical wave equationAsymptotic stability of solitons for mKdVConstruction of multi-solitons and multi kink-solitons of derivative nonlinear Schrödinger equationsOrbital stability of the sum of smooth solitons in the Degasperis-Procesi equationAttractors of Hamilton nonlinear PDEsRecent results for the Landau-Lifshitz equationOrbital stability of double solitons for the Benjamin-Ono equationConstruction of multi-solitons for the energy-critical wave equation in dimension 5Construction of solutions to the subcritical gKdV equations with a given asymptotical behaviorAsymptotic stability of Zakharov-Kuznetsov solitonsStability of solitons of the Landau-Lifshitz equation with planar anisotropyMulti-Solitary Waves for the Nonlinear Klein-Gordon EquationUnnamed ItemLeapfrogging vortex rings for the three dimensional Gross-Pitaevskii equationAsymptotic stability of solitons for the Benjamin-Ono equationStability of peakons for an integrable modified Camassa-Holm equation with cubic nonlinearityMulti solitary waves for nonlinear Schrödinger equationsConstruction of Multibubble Solutions for the Critical GKDV EquationExistence of multi-solitons for the focusing logarithmic non-linear Schrödinger equationNonlinear stability of MKdV breathersOrbital stability of a sum of solitons and breathers of the modified Korteweg–de Vries equationAsymptotic stability of the black soliton for the Gross–Pitaevskii equationOrbital stability of the sum of \(N\) peakons for the Dullin-Gottwald-Holm equationNonlinear stability of Gardner breathersOn the orbital stability of the Degasperis-Procesi antipeakon-peakon profileStability of peakons for the Novikov equationStability of the sum of two solitary waves for (gDNLS) in the energy spaceNonlinear stability of 2-solitons of the sine-Gordon equation in the energy spaceThe focusing logarithmic Schrödinger equation: analysis of breathers and nonlinear superpositionStrongly interacting multi-solitons with logarithmic relative distance for the gKdV equationAttractors of nonlinear Hamiltonian partial differential equationsDynamical stability of the train of smooth solitary waves to the generalized two-component Camassa-Holm systemAsymptotic stability of \(N\)-solitary waves of the FPU latticesInelastic interaction of nearly equal solitons for the quartic gKdV equationNonexistence of pure multi-solitons for the quartic gBBM equationStability of periodic peakons for the modified \(\mu \)-Camassa-Holm equationOrbital stability of periodic peakons to a generalized \(\mu\)-Camassa-Holm equationDescription of two soliton collision for the quartic gKdV equationAsymptotic stability of the Toda \(m\)-solitonInstability of the solitary waves for the generalized derivative nonlinear Schrödinger equation in the degenerate caseOrbital stability of the train of peakons for an integrable modified Camassa-Holm equationStability in the energy space for chains of solitons of the Landau-Lifshitz equationMulti-soliton-type solutions of the generalized KdV equationsStability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equationOn the asymptotic stability in the energy space for multi-solitons of the Landau-Lifshitz equationSoliton resolution for the focusing modified KdV equationStability of the multi-solitons of the modified Korteweg–de Vries equation *Stability in the energy space of the sum of N peakons for a modified Camassa-Holm equation with higher-order nonlinearityThe orbital stability of the ground states and the singularity formation for the gravitational Vlasov-Poisson systemThe Gardner equation and the 𝐿²-stability of the 𝑁-soliton solution of the Korteweg-de Vries equationStability of the traveling waves for the derivative Schrödinger equation in the energy spaceConstruction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equationsAsymptotic stability of solitons of the gKdV equations with general nonlinearityGlobal attractor for weakly damped gKdV equations in higher Sobolev spacesSmoothness and Exponential Decay ofL2-Compact Solutions of the Generalized KdV EquationsDescription of the inelastic collision of two solitary waves for the BBM equationStability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equationsStability of multipeakonsInelastic character of solitons of slowly varying gKdV equationsA Liouville property with application to asymptotic stability for the Camassa-Holm equationInitial boundary value problems for some nonlinear dispersive models on the half-line: a review and open problemsStability of KdV solitons on the half-lineOrbital and asymptotic stability of a train of peakons for the Novikov equationConstruction of solutions to the \(L^2\)-critical KdV equation with a given asymptotic behaviourA rigidity result for the Holm-Staley \(b\)-family of equations with application to the asymptotic stability of the Degasperis-Procesi peakonStability of two soliton collision for nonintegrable gKdV equationsRefined Jacobian estimates and Gross-Pitaevsky vortex dynamicsRandom modulation of solitons for the stochastic Korteweg-de Vries equationOrbital Stability: Analysis Meets GeometryConditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearityNon dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitonsConstruction of 2-solitons with logarithmic distance for the one-dimensional cubic Schrödinger systemDescription and classification of \(2\)-solitary waves for nonlinear damped Klein-Gordon equationsMulti-Soliton Solutions for the Supercritical gKdV EquationsSolution to the semilinear wave equation with a pyramid-shaped blow-up surfaceOn asymptotic stability of nonlinear wavesStrongly interacting kink-antikink pairs for the scalar field equation in dimension \(1+1\)Kink networks for scalar fields in dimension \(1 + 1\)Asymptotic stability of the Degasperis-Procesi antipeakon-peakon profileAsymptotic two-soliton solutions in the Fermi-Pasta-Ulam model




This page was built for publication: Stability and asymptotic stability for subcritical gKdV equations