Periodic Waves of the Modified KdV Equation as Minimizers of a New Variational Problem
DOI10.1137/21M1465329zbMath1503.35200arXiv2112.05231MaRDI QIDQ5056848
Publication date: 8 December 2022
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.05231
KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25) Variational methods applied to problems in fluid mechanics (76M30) Soliton equations (35Q51) Bifurcations in context of PDEs (35B32) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Elliptic functions and integrals (33E05) PDE constrained optimization (numerical aspects) (49M41)
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Cites Work
- Unnamed Item
- On the instability of periodic waves for dispersive equations.
- Nonlinear stability of periodic traveling wave solutions to the Schrödinger and the modified Korteweg-de Vries equations
- On the spectra of periodic waves for infinite-dimensional Hamiltonian systems
- On the number of critical points of the period
- Remark on the number of critical points of the period
- Periodic waves in the fractional modified Korteweg-de Vries equation
- Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background
- Monotonicity of the period function for \(u-u+u^p=0\) with \(p\in \mathbb R\) and \(p>1\)
- Orbital stability of one-parameter periodic traveling waves for dispersive equations and applications
- On the Spectral and Orbital Stability of Spatially Periodic Stationary Solutions of Generalized Korteweg-de Vries Equations
- Nonlinear Wave Equations for Oceanic Internal Solitary Waves
- Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
- The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation
- Internal Gravity Waves
- An index theorem for the stability of periodic travelling waves of Korteweg–de Vries type
- Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg–de Vries Equation
- Stability of periodic waves for the fractional KdV and NLS equations
- On the stability of solitary wave solutions for a generalized fractional Benjamin–Bona–Mahony equation
- Spectral Stability of Nonlinear Waves in KdV‐Type Evolution Equations
- Interfacial long traveling waves in a two‐layer fluid with variable depth
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