The Small Dispersion Limit of the Benjamin-Ono Equation and the Evolution of a Step Initial Condition

DOI10.1143/JPSJ.67.1814zbMath0978.76016MaRDI QIDQ4491483

Yoshimasa Matsuno

Publication date: 26 July 2000

Published in: Journal of the Physical Society of Japan (Search for Journal in Brave)

zbMATH Keywords

asymptotic solutionBenjamin-Ono equationsmall dispersion limitWhitham modulation theorystep initial conditioninternal bore wavetrain of solitary waves

Mathematics Subject Classification ID

Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Solitary waves for incompressible inviscid fluids (76B25) Internal waves for incompressible inviscid fluids (76B55) Soliton equations (35Q51)

Related Items (8)

Lax Eigenvalues in the Zero-Dispersion Limit for the Benjamin–Ono Equation on the Torus ⋮ 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 ⋮ Dispersive shock waves in systems with nonlocal dispersion of Benjamin–Ono type ⋮ On the generation of dispersive shock waves ⋮ The scattering transform for the Benjamin-Ono equation in the small-dispersion limit ⋮ On the zero-dispersion limit of the benjamin-ono cauchy problem for positive initial data ⋮ Asymptotic solutions of the nonlocal nonlinear Schrödinger equation in the limit of small dispersion

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