New variational characterization of periodic waves in the fractional Korteweg-de Vries equation
arXiv:1907.01412 · doi:10.1088/1361-6544/ab6a79
Abstract
Periodic waves in the fractional Korteweg-de Vries equation have been previously characterized as constrained minimizers of energy subject to fixed momentum and mass. Here we characterize these periodic waves as constrained minimizers of the quadratic form of energy subject to fixed cubic part of energy and the zero mean. This new variational characterization allows us to unfold the existence region of travelling periodic waves and to give a sharp criterion for spectral stability of periodic waves with respect to perturbations of the same period. The sharp stability criterion is given by the monotonicity of the map from the wave speed to the wave momentum similarly to the stability criterion for solitary waves.
28 pages
References in corpus (6)
- Stability properties of solitary waves for fractional KdV and BBM equations
- Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
- Counting unstable eigenvalues in Hamiltonian spectral problems via commuting operators
- A Hamiltonian-Krein (instability) index theory for KdV-like eigenvalue problems
- Nondegeneracy and Stability of Antiperiodic Bound States for Fractional Nonlinear Schrödinger Equations
- Waves of maximal height for a class of nonlocal equations with homogeneous symbols