Breathers and the dynamics of solutions in KdV type equations

DOI10.1007/s00220-018-3206-9zbMath1427.76044arXiv1803.05475OpenAlexW3104958739MaRDI QIDQ1741659

Claudio Muñoz, Gustavo Ponce

Publication date: 6 May 2019

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

Full work available at URL: https://arxiv.org/abs/1803.05475

zbMATH Keywords

nonexistencescatteringtime-periodic solutiondispersive region

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (17)

A mixed approximate method to simulate generalized Hirota-Satsuma coupled KdV equations ⋮ Asymptotic Stability of KdV Solitons on the Half-Line: A Study in the Energy Space ⋮ The multi elliptic‐localized solutions and their asymptotic behaviors for the mKdV equation ⋮ Global solutions and stability properties of the 5th order Gardner equation ⋮ Full family of flattening solitary waves for the critical generalized KdV equation ⋮ On long-time behavior for solutions of the Gear-Grimshaw system ⋮ Dynamics of breathers in the Gardner hierarchy: universality of the variational characterization ⋮ Extended Decay Properties for Generalized BBM Equation ⋮ On local energy decay for large solutions of the Zakharov-Kuznetsov equation ⋮ Asymptotic behavior of solutions of the dispersion generalized Benjamin-Ono equation ⋮ On the Long Time Behavior of Solutions to the Intermediate Long Wave Equation ⋮ Decay of small odd solutions for long range Schrödinger and Hartree equations in one dimension ⋮ Asymptotic dynamics for the small data weakly dispersive one-dimensional Hamiltonian ABCD system ⋮ On the asymptotic behavior of solutions to the Benjamin-Ono equation ⋮ Stability of mKdV breathers on the half-line ⋮ Variational methods for breather solutions of nonlinear wave equations ⋮ On Long Time Behavior of Solutions of the Schrödinger--Korteweg--de Vries System

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On decay properties of solutions of the \(k\)-generalized KdV equation
• Nonlinear stability of MKdV breathers
• Description of two soliton collision for the quartic gKdV equation
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Construction of solutions to the subcritical gKdV equations with a given asymptotical behavior
• Scattering for the quartic generalised Korteweg-de Vries equation
• On uniqueness properties of solutions of the \(k\)-generalized KdV equations
• Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
• Large time asymptotics of solutions to the generalized Korteweg-de Vries equation
• A Liouville theorem for the critical generalized Korteweg-de Vries equation
• Scattering in the energy space for Boussinesq equations
• Nonlinear stability of Gardner breathers
• Nonlinear small data scattering for the generalized Korteweg-de Vries equation
• Small data scattering and soliton stability in \(\dot{H}^{-1/6}\) for the quartic KdV equation
• Structural transformation of eigenvalues for a perturbed algebraic soliton potential.
• On asymptotic stability of nonlinear waves
• The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space
• Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers
• The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
• Nonexistence of small, odd breathers for a class of nonlinear wave equations
• Asymptotic stability of solitons for mKdV
• The Modified Korteweg-de Vries Equation
• Long time behavior of solutions to the mKdV
• Lower bounds for non-trivial travelling wave solutions of equations of KdV type
• Kink dynamics in the $\phi ^4$ model: Asymptotic stability for odd perturbations in the energy space
• On the Inelastic Two-Soliton Collision for gKdV Equations with General Nonlinearity
• The emergence of solitons of the korteweg-de vries equation from arbitrary initial conditions
• The collisionless shock region for the long‐time behavior of solutions of the KdV equation
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Blow up in finite time and dynamics of blow up solutions for the 𝐿²–critical generalized KdV equation
• Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear electrodynamics
• Asymptotic stability of solitons of the subcritical gKdV equations revisited
• The Gardner equation and the 𝐿²-stability of the 𝑁-soliton solution of the Korteweg-de Vries equation
• Extended Decay Properties for Generalized BBM Equation

This page was built for publication: Breathers and the dynamics of solutions in KdV type equations