Breakdown of the Whitham Modulation Theory and the Emergence of Dispersion

DOI10.1111/sapm.12086zbMath1338.35387OpenAlexW1557335111MaRDI QIDQ2807454

Thomas J. Bridges

Publication date: 25 May 2016

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/sapm.12086

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Traveling wave solutions (35C07)

Related Items (2)

Whitham modulation equations, coalescing characteristics, and dispersive Boussinesq dynamics ⋮ A high-order nonlinear Schrödinger equation as a variational problem for the averaged Lagrangian of the nonlinear Klein-Gordon equation

Cites Work

• On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions
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• Modulation instability: The beginning
• Validity of Whitham's equations for the modulation of periodic traveling waves in the NLS equation
• Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation
• Two-timing, variational principles and waves
• On the superharmonic instability of surface gravity waves on fluid of finite depth
• Multisymplectic structures and the variational bicomplex
• Rigorous Justification of the Whitham Modulation Equations for the Generalized Korteweg-de Vries Equation
• The superharmonic instability of finite-amplitude water waves
• The classification of 2 × 2 systems of non-strictly hyperbolic conservation laws, with application to oil recovery
• Nonlinear deep water waves: Theory and experiment
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• Multi-symplectic structures and wave propagation
• Unified approach to KdV modulations
• Non-linear dispersive waves
• A universal form for the emergence of the Korteweg–de Vries equation
• Whitham's modulation equations and stability of periodic wave solutions of the Korteweg-de Vries-Kuramoto-Sivashinsky Equation
• Contributions to the Theory of Waves in Non-linear Dispersive Systems
• Hyperbolic conservation laws with umbilic degeneracy

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