Multi-phase solutions of the Benjamin-Ono equation and their averaging

DOI10.1007/BF01156581zbMath0752.35058MaRDI QIDQ1177817

I. M. Krichever, S. Yu. Dobrokhotov

Publication date: 26 June 1992

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

quasiperiodic solutionsfinite-zone integration

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Integro-partial differential equations (45K05) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (23)

On the Benjamin-Ono equation on \(\mathbb{T}\) and its periodic and quasiperiodic solutions ⋮ Complete integrability of the Benjamin-Ono equation on the multi-soliton manifolds ⋮ Remark on the phase shift in the Kuzmak-Whitham ansatz ⋮ Multiphase solutions and their reductions for a nonlocal nonlinear Schrödinger equation with focusing nonlinearity ⋮ Quasilinear systems with linearizable characteristic webs ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. II: Dynamics ⋮ Asymptotic multiscale solutions to Navier-Stokes equations with fast oscillating perturbations in boundary layers ⋮ Hyperbolicity of the modulation equations for the Serre-Green-Naghdi model ⋮ Finite gap conditions and small dispersion asymptotics for the classical periodic Benjamin–Ono equation ⋮ The multi-dimensional Hamiltonian structures in the Whitham method ⋮ Modulation theory, dispersive shock waves and Gerald Beresford Whitham ⋮ On the generation of dispersive shock waves ⋮ The scattering transform for the Benjamin-Ono equation in the small-dispersion limit ⋮ On the minimal set of conservation laws and the Hamiltonian structure of the Whitham equations ⋮ Spatially quasi-periodic water waves of infinite depth ⋮ Computation of time-periodic solutions of the Benjamin-Ono equation ⋮ On the zero-dispersion limit of the benjamin-ono cauchy problem for positive initial data ⋮ Exact Bohr-Sommerfeld conditions for the quantum periodic Benjamin-Ono equation ⋮ On the canonical forms of the multi-dimensional averaged Poisson brackets ⋮ Modulation solutions for the Benjamin-Ono equation ⋮ Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data ⋮ Quasi-periodic travelling gravity–capillary waves

Cites Work

• On the development of large-sized short-scaled disturbances in boundary layers
• The Modulated Phase Shift for Weakly Dissipated Nonlinear Oscillatory Waves of the Korteweg-deVries Type
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
• Internal waves of permanent form in fluids of great depth
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