Nonlinear stability of Gardner breathers
From MaRDI portal
Publication:1680468
DOI10.1016/j.jde.2017.09.035zbMath1378.35259arXiv1705.04206OpenAlexW2964094531MaRDI QIDQ1680468
Publication date: 16 November 2017
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1705.04206
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Variational methods applied to PDEs (35A15) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)
Related Items
Breather solutions of a negative order modified Korteweg-de Vries equation and its nonlinear stability ⋮ Focusing and defocusing mKdV equations with nonzero boundary conditions: inverse scattering transforms and soliton interactions ⋮ Global solutions and stability properties of the 5th order Gardner equation ⋮ Existence of single-peak solitary waves and double-peaks solitary wave of Gardner equation with Kuramoto-Sivashinsky perturbation ⋮ On long-time behavior for solutions of the Gear-Grimshaw system ⋮ Dynamics of breathers in the Gardner hierarchy: universality of the variational characterization ⋮ Nonlinear stability of breather solutions to the coupled modified Korteweg-de Vries equations ⋮ Breathers and the dynamics of solutions in KdV type equations ⋮ The Akhmediev breather is unstable ⋮ The essential spectrum of periodically stationary solutions of the complex Ginzburg-Landau equation ⋮ The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space ⋮ Stability of mKdV breathers on the half-line ⋮ Variational methods for breather solutions of nonlinear wave equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The Gardner equation and the stability of multi-kink solutions of the mKdV equation
- On the ill-posedness of the Gardner equation
- Effective dynamics of double solitons for perturbed mKdV
- Well-posedness and stability results for the Gardner equation
- Stability of detonation profiles in the ZND limit
- Stability of two soliton collision for nonintegrable gKdV equations
- Dispersive blow-up for nonlinear Schrödinger equations revisited
- Bilinear transformation method
- Stability theory of solitary waves in the presence of symmetry. I
- On the stability of travelling waves in weighted \(L^ \infty\) spaces
- Asymptotic stability of solitary waves
- Structure of linearization operators of the Korteweg-de Vries hierarchy equations expanded around single-soliton solutions
- On the ill-posedness of some canonical dispersive equations.
- Stability and asymptotic stability for subcritical gKdV equations
- Spectral and dynamical stability of nonlinear waves
- Structural transformation of eigenvalues for a perturbed algebraic soliton potential.
- Nonexistence of small, odd breathers for a class of nonlinear wave equations
- Stability of undercompressive shock profiles
- On the variational structure of breather solutions. I: Sine-Gordon equation
- Complete eigenfunctions of linearized integrable equations expanded around a soliton solution
- Focusing mKdV Breather Solutions with Nonvanishing Boundary Condition by the Inverse Scattering Method
- Kink dynamics in the $\phi ^4$ model: Asymptotic stability for odd perturbations in the energy space
- Spectra of positive and negative energies in the linearized NLS problem
- An Oscillation Method for Fourth-Order, Selfadjoint, Two-Point Boundary Value Problems with Nonlinear Eigenvalues
- On the stability ofN-solitons in integrable systems
- Modulational Stability of Ground States of Nonlinear Schrödinger Equations
- Lyapunov stability of ground states of nonlinear dispersive evolution equations
- Stability and instability of solitary waves of Korteweg-de Vries type
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- On the stability of KdV multi‐solitons
- Stability of multiple-pulse solutions
- Purely nonlinear instability of standing waves with minimal energy
- Instability in nonlinear Schrödinger breathers
- On the nonlinear stability of mKdV breathers
- Asymptotic stability of solitons of the subcritical gKdV equations revisited
- Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
- Stability and Evolution of Solitary Waves in Perturbed Generalized Nonlinear Schrödinger Equations
- Generation of solitons and breathers in the extended Korteweg–de Vries equation with positive cubic nonlinearity
- Integrals of nonlinear equations of evolution and solitary waves
- Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
- Asymptotic stability of solitons for subcritical generalized KdV equations
This page was built for publication: Nonlinear stability of Gardner breathers
