On the zero-dispersion limit of the benjamin-ono cauchy problem for positive initial data

DOI10.1002/cpa.20345zbMath1213.35052arXiv1002.3178OpenAlexW2022837827MaRDI QIDQ3068376

Zhengjie Xu, Peter D. Miller

Publication date: 14 January 2011

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.3178

zbMATH Keywords

integrabilitysingular limitsWitham equationsdispersive shockdissipationless Burgers equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Singular perturbations in context of PDEs (35B25) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Stratification effects in inviscid fluids (76B70)

Related Items (14)

Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions ⋮ Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study ⋮ Lax Eigenvalues in the Zero-Dispersion Limit for the Benjamin–Ono Equation on the Torus ⋮ Zero-dispersion limit for the Benjamin-Ono equation on the torus with bell shaped initial data ⋮ Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ Finite gap conditions and small dispersion asymptotics for the classical periodic Benjamin–Ono equation ⋮ Modulated equations of Hamiltonian PDEs and dispersive shocks ⋮ Dispersive shock waves in systems with nonlocal dispersion of Benjamin–Ono type ⋮ Some open problems in random matrix theory and the theory of integrable systems. II ⋮ On the generation of dispersive shock waves ⋮ The scattering transform for the Benjamin-Ono equation in the small-dispersion limit ⋮ Simplicity and Finiteness of Discrete Spectrum of the Benjamin--Ono Scattering Operator ⋮ Critical behavior for scalar nonlinear waves

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