Bifurcations of new eigenvalues for the Benjamin–Ono equation

DOI10.1063/1.532665zbMath0932.35183OpenAlexW2083183096MaRDI QIDQ4701582

Dmitry E. Pelinovsky, Catherine Sulem

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532665

zbMATH Keywords

inverse scattering transformsoliton potentialssoliton generationlinear scattering problemintegro-differential Benjamin-Ono equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Internal waves for incompressible inviscid fluids (76B55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Bifurcations in context of PDEs (35B32)

Related Items (7)

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study ⋮ Dark soliton generation for the intermediate nonlinear Schrödinger equation ⋮ Perturbations of embedded eigenvalues for the planar bilaplacian ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ Linear stability of multiple dark solitary wave solutions of a nonlocal nonlinear Schrödinger equation for envelope waves ⋮ Asymptotic approximation for a new eigenvalue in linear problems without a threshold ⋮ Dispersive focusing in fractional Korteweg–de Vries-type equations

Cites Work

• The Benjamin-Ono equation recursivity of linearization maps - Lax pairs
• Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case
• A note on the numerical and \(N\)-soliton solutions of the Benjamin-Ono evolution equation
• Complete integrability of the Benjamin-Ono equation by means of action-angle variables
• Variationally obtained approximate eigenvalues of the Zakharov-Shabat scattering problem for real potentials.
• The small dispersion limit of the Korteweg-de Vries equation. III
• On the limit from the intermediate long wave equation to the Benjamin–Ono equation
• The scattering transform for the Benjamin-Ono equation
• Weakly bound states in dimensions
• Direct and inverse scattering problems of the nonlinear intermediate long wave equation
• Internal wave solitons
• Initial value problem of the linearized Benjamin–Ono equation and its applications
• Solutions to the Time Dependent Schrödinger and the Kadomtsev-Petviashvili Equations
• Eigenvalues, and instabilities of solitary waves
• The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
• On the initial value problem for the modified Benjamin–Ono equation

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