On the Elliptic-Hyperbolic Transition in Whitham Modulation Theory
From MaRDI portal
Publication:4594899
DOI10.1137/17M1111437zbMath1375.74047MaRDI QIDQ4594899
Daniel J. Ratliff, Thomas J. Bridges
Publication date: 27 November 2017
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Nonlinear waves in solid mechanics (74J30) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05)
Related Items
Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory ⋮ Phase dynamics of the Dysthe equation and the bifurcation of plane waves ⋮ Initial-boundary value problem for stimulated Raman scattering model: solvability of Whitham type system of equations arising in long-time asymptotic analysis ⋮ Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory ⋮ The modulation of multiple phases leading to the modified Korteweg–de Vries equation ⋮ A high-order nonlinear Schrödinger equation as a variational problem for the averaged Lagrangian of the nonlinear Klein-Gordon equation ⋮ Dispersive dynamics in the characteristic moving frame ⋮ Genuine nonlinearity and its connection to the modified Korteweg–de Vries equation in phase dynamics
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol'd
- On polynomial mappings from the plane to the plane
- Modulation instability: The beginning
- Validity of Whitham's equations for the modulation of periodic traveling waves in the NLS equation
- Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation
- The Boussinesq equation revisited
- Multisymplectic geometry, local conservation laws and Fourier pseudospectral discretization for the ``good Boussinesq equation
- Dispersive hydrodynamics: Preface
- Modulation theory, dispersive shock waves and Gerald Beresford Whitham
- Whitham modulation equations, coalescing characteristics, and dispersive Boussinesq dynamics
- Group velocity and nonlinear dispersive wave propagation
- Multisymplectic structures and the variational bicomplex
- Soliton and antisoliton interactions in the ‘‘good’’ Boussinesq equation
- Instabilities of finite-amplitude water waves
- The instabilities of gravity waves of finite amplitude in deep water II. Subharmonics
- Integral properties of periodic gravity waves of finite amplitude
- On the modulation of water waves in the neighbourhood of kh ≈ 1.363
- Finite-amplitude deep-water waves on currents
- Reappraisal of the Kelvin–Helmholtz problem. Part 1. Hamiltonian structure
- A general approach to linear and non-linear dispersive waves using a Lagrangian
- A universal form for the emergence of the Korteweg–de Vries equation
- Phase dynamics of periodic waves leading to the Kadomtsev–Petviashvili equation in 3+1 dimensions
- Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg–de Vries equation
- Modulations of viscous fluid conduit periodic waves
- A perturbation method for nonlinear dispersive wave problems
- The disintegration of wave trains on deep water Part 1. Theory
- Contributions to the Theory of Waves in Non-linear Dispersive Systems
- Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices
- The symplectic Evans matrix, and the instability of solitary waves and fronts
This page was built for publication: On the Elliptic-Hyperbolic Transition in Whitham Modulation Theory