Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE
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Publication:5115055
DOI10.1007/978-1-4939-9806-7_3zbMath1442.35355arXiv1811.08652OpenAlexW2900874300MaRDI QIDQ5115055
Publication date: 29 June 2020
Published in: Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1811.08652
PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)
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Cites Work
- The Benjamin-Ono hierarchy with asymptotically reflectionless initial data in the zero-dispersion limit
- Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
- Intermediate long-wave equation on a half-line
- Invariant measures and long time behaviour for the Benjamin-Ono equation. II.
- Blow up for the critical gKdV equation. II: Minimal mass dynamics
- Invariant measures and long time behaviour for the Benjamin-Ono equation. III
- Remarks on the orbital stability of ground state solutions of fKdV and related equations
- Improvement of the energy method for strongly nonresonant dispersive equations and applications
- Stability properties of periodic traveling waves for the intermediate long wave equation
- On the long time behavior of a generalized KdV equation
- On the stability of KdV multi-solitons.
- The IVP for the Benjamin-Ono equation in weighted Sobolev spaces
- Well-posedness for a higher-order Benjamin-Ono equation
- Large-time asymptotics of the generalized Benjamin-Ono-Burgers equation
- Global well-posedness for the KP-II equation on the background of a non-localized solution
- Local well-posedness and blow-up in the energy space for a class of \(L^2\) critical dispersion generalized Benjamin-Ono equations
- Stability of the line soliton of the KP-II equation under periodic transverse perturbations
- The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. II.
- Generalized internal long waves equations: Construction, Hamiltonian structure, and conservation laws
- Bilinear transformation method
- On the global well-posedness of the Benjamin-Ono equation
- Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation
- Orbital stability of double solitons for the Benjamin-Ono equation
- Global well-posedness in the energy space for the Benjamin-Ono equation on the circle
- Control and stabilization of the Benjamin-Ono equation in \(L^2(\mathbb T)\)
- On the propagation of regularities in solutions of the Benjamin-Ono equation
- Nonlocal models for nonlinear, dispersive waves
- Asymptotic models for internal waves
- On the Cauchy problem for higher-order nonlinear dispersive equations
- Benjamin-Ono equation on a half-line
- A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- The Benjamin-Ono-Burgers equation: An application in solar physics
- On the stability of nonlinear waves in integrable models
- The Benjamin-Ono equation recursivity of linearization maps - Lax pairs
- Sufficient conditions for stability of solitary-wave solutions of model equations for long waves
- Asymptotic analysis of soliton problems. An inverse scattering approach
- On the number of solitons for the intermediate long wave equation
- Sur quelques généralisations de l'équation de Korteweg-de Vries
- Temporal asymptotic behaviour of solutions of the Benjamin-Ono-Burgers equation
- The Benjamin-Ono equation in weighted Sobolev spaces
- Multi-phase solutions of the Benjamin-Ono equation and their averaging
- Smoothing properties and existence of solutions for the generalized Benjamin-Ono equation
- Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane
- Who cares about integrability?
- Smoothing properties and retarded estimates for some dispersive evolution equations
- A note on the numerical and \(N\)-soliton solutions of the Benjamin-Ono evolution equation
- Existence and stability of solitary wave solutions of the Benjamin equation
- \(L^2\) global well-posedness of the initial value problem associated to the Benjamin equation
- On the exact solutions of the intermediate long-wave equation
- On the stability of solitary-wave solutions of model equations for long waves
- Long-time asymptotics for integrable systems. Higher order theory
- On the reduction of the modified Benjamin-Ono equation to the cubic derivative nonlinear Schrödinger equation
- Solitary waves of generalized Kadomtsev-Petviashvili equations
- Decay and analyticity of solitary waves
- Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
- Consistency of the KP approximation
- On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations
- Stability and symmetry of solitary-wave solutions to systems modeling interactions of long waves
- Benjamin-Ono equation with unbounded data
- Eigenfunctions and eigenvalues for a scalar Riemann-Hilbert problem associated to inverse scattering
- Numerical solution of some nonlocal, nonlinear dispersive wave equations
- On well-posedness for some dispersive perturbations of Burgers' equation
- Invariant measure and long time behavior of regular solutions of the Benjamin-Ono equation
- Modulation solutions for the Benjamin-Ono equation
- Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
- Integrable systems and their recursion operators.
- A stability criterion for two-fluid interfaces and applications
- The Cauchy problem for the Benjamin-Ono equation in \(L^{2}\) revisited
- Complete integrability of the Benjamin-Ono equation by means of action-angle variables
- Linear stability of multiple internal solitary waves in fluids of great depth
- On the generation of dispersive shock waves
- The scattering transform for the Benjamin-Ono equation in the small-dispersion limit
- Decay of Benjamin-Ono solitons under the influence of dissipation
- Invariance of the Gibbs measure for the Benjamin-Ono equation
- A numerical approach to blow-up issues for dispersive perturbations of Burgers' equation
- Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg-de Vries equations
- A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
- Unique continuation principles for the Benjamin-Ono equation
- Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation
- On decay properties of solutions to the IVP for the Benjamin-Ono equation
- The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces
- On the N-tuple wave solutions of the Korteweg-de Vries equation
- Asymptotic stability of solitons for the Benjamin-Ono equation
- Ill-Posedness Issues for the Benjamin--Ono and Related Equations
- IST Versus PDE: A Comparative Study
- Simplicity and Finiteness of Discrete Spectrum of the Benjamin--Ono Scattering Operator
- Effect of Viscosity on Long Gravity Waves
- Algebraic Solitary Waves in Stratified Fluids
- Bäcklund Transform and Conservation Laws of the Benjamin-Ono Equation
- A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution
- N-Periodic Wave and N-Soliton Solutions of the Modified Benjamin-Ono Equation
- Solutions of the Higher Order Benjamin-Ono Equation
- Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data
- A note on the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space
- Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
- Intermediate long wave systems for internal waves
- Invariant Measures and Long-Time Behavior for the Benjamin–Ono Equation
- Stability of line solitons for the KP-II equation in ℝ²
- Two-dimensional interactions of solitons in a two-layer fluid of finite depth
- Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation
- Strong Interactions between Solitary Waves Belonging to Different Wave Modes
- Total Positivity and the Stability of Internal Waves in Stratified Fluids of Finite Depth
- Control and stabilization of the Benjamin-Ono equation on a periodic domain
- Remarks on the Mass Constraint for KP-Type Equations
- Oblique interactions of weakly nonlinear long waves in dispersive systems
- LONG NONLINEAR INTERNAL WAVES
- Dispersive Perturbations of Burgers and Hyperbolic Equations I: Local Theory
- Why are solitons stable?
- Internal waves of permanent form in fluids of great depth
- Solitary internal waves in deep water
- Variational methods and applications to water waves
- Nonlinear Theory of Ion Acoustic Waves with Landau Damping
- Nonlinear Kelvin and continental-shelf waves
- Hamiltonian long‐wave expansions for free surfaces and interfaces
- Long nonlinear waves in stratified shear flows
- Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations
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- A Para-Differential Renormalization Technique for Nonlinear Dispersive Equations
- On the zero-dispersion limit of the benjamin-ono cauchy problem for positive initial data
- The small dispersion limit of the Korteweg-de Vries equation. I
- On the limit from the intermediate long wave equation to the Benjamin–Ono equation
- Weak and Strong Interactions between Internal Solitary Waves
- The scattering transform for the Benjamin-Ono equation
- On the controllability and stabilization of the linearized Benjamin-Ono equation
- Soliton Interactions of the Kadomtsev-Petviashvili Equation and Generation of Large-Amplitude Water Waves
- Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
- Global wellposedness of the modified Benjamin-Ono equation with initial data in H1/2
- Weakly transverse Boussinesq systems and the Kadomtsev–Petviashvili approximation
- Global well-posedness of the Benjamin–Ono equation in low-regularity spaces
- An application of the inverse scattering transform to the modified intermediate long wave equation
- The Lyapunov stability of the N-soliton solutions in the Lax hierarchy of the Benjamin-Ono equation
- The korteweg-de vries equation with small dispersion: Higher order lax-levermore theory
- Global well-posedness in <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for the periodic Benjamin-Ono equation
- On interfacial gravity-capillary solitary waves of the Benjamin type and their stability
- Positivity Properties of the Fourier Transform and the Stability of Periodic Travelling-Wave Solutions
- Soliton Solutions of the KP Equation and Application to Shallow Water Waves
- Soliton models of long internal waves
- Scattering and inverse scattering for first order systems
- The stability of internal solitary waves
- On a Bäcklund transformation and scattering problem for the modified intermediate long wave equation
- On the cauchy problem for the benjamin-ono equation
- Stability and instability of solitary waves of Korteweg-de Vries type
- New integrable nonlinear integrodifferential equations and related solvable finite-dimensional dynamical systems
- Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation
- Local Smoothing Properties of Dispersive Equations
- Properties of the Benjamin–Ono equation
- Interaction of the Benjamin-Ono solitons
- Conservation laws of the Benjamin–Ono equation
- Resonant Transfer of Energy between Nonlinear Waves in Neighboring Pycnoclines
- Long Internal Waves in Fluids of Great Depth
- The N -soliton solution of the Benjamin-Ono equation
- An investigation of internal solitary waves in a two-fluid system
- Direct and inverse scattering problems of the nonlinear intermediate long wave equation
- On the periodic intermediate long wave equation
- Positivity Properties and Stability of Solitary–Wave Solutions of Model Equations For Long Waves
- Periodic solutions of the intermediate long-wave equation: a nonlinear superposition principle
- The dissipation of nonlinear dispersive waves: the case of asymptotically weak nonlinearity
- A new kind of solitary wave
- The initial-value problem for the Korteweg-de Vries equation
- Resonantly interacting solitary waves
- Obliquely interacting solitary waves
- Lagrange multiplier formalism for a spin-3/2 field
- Multi-soliton solutions in a finite depth fluid
- Multi-soliton-like solutions to the Benjamin–Ono equation
- The Propagation of Long Large Amplitude Internal Waves
- Benjamin—Ono-related equations and their solutions
- Exact multi-soliton solution of the Benjamin-Ono equation
- On periodic and solitary wavelike solutions of the intermediate long-wave equation
- Large time asymptotics of solutions to the generalized Benjamin-Ono equation
- Oblique interaction of interfacial solitary waves in a two-layer deep fluid
- Perturbation theory for the Benjamin-Ono equation
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- On the Generalized Benjamin-Ono Equation
- On the stability of KdV multi‐solitons
- Oblique Interactions between Internal Solitary Waves
- Stability of Nonlinear Periodic Internal Waves in a Deep Stratified Fluid
- Model equations for waves in stratified fluids
- Initial value problem of the linearized Benjamin–Ono equation and its applications
- An extension of the steepest descent method for Riemann-Hilbert problems: The small dispersion limit of the Korteweg-de Vries (KdV) equation
- GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H1(R)
- The Small Dispersion Limit of the Benjamin-Ono Equation and the Evolution of a Step Initial Condition
- The Cauchy Problem for the Fractional Kadomtsev--Petviashvili Equations
- Small data global solutions for the Camassa–Choi equations
- Jost Solutions and the Direct Scattering Problem of the Benjamin--Ono Equation
- Stability properties of solitary waves for fractional KdV and BBM equations
- On the modified intermediate long-wave equation
- Dispersive shock waves in systems with nonlocal dispersion of Benjamin–Ono type
- Asymptotic stability of solitons of the subcritical gKdV equations revisited
- Bifurcations of new eigenvalues for the Benjamin–Ono equation
- Solitary-Wave Solutions of the Benjamin Equation
- Uniqueness of Benjamin's Solitary-Wave Solution of the Benjamin-Ono Equation
- Weakly nonlinear internal waves in a two-fluid system
- Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems
- The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
- Weakly interacting internal solitary waves in neighbouring pycnoclines
- The Inverse Scattering Transform for the Benjamin–Ono Equation
- Oblique interaction of internal solitary waves in a two-layer fluid of infinite depth
- On the initial value problem for the modified Benjamin–Ono equation
- Dilation method and smoothing effects of solutions to the Benjamin–Ono equation
- Solitary and periodic waves of a new kind
- Global Well-Posedness and Limit Behavior for a Higher-Order Benjamin-Ono Equation
