Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study (Q2133012)

scientific article; zbMATH DE number 7515841

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English	Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study	scientific article; zbMATH DE number 7515841

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instance of

scholarly article

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title

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study (English)

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Journal of Computational Physics

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publication date

29 April 2022

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full work available at URL

https://arxiv.org/abs/2012.03336

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zbMATH Keywords

Benjamin-Ono equation

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solitary wave

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soliton resolution

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ground state

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rational basis

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blow-up

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describes a project that uses

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Nonlocal models for nonlinear, dispersive waves

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Sufficient conditions for stability of solitary-wave solutions of model equations for long waves

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Model equations for waves in stratified fluids

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Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane

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Scaling, stability and singularities for nonlinear, dispersive wave equations: the critical case

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Internal waves of permanent form in fluids of great depth

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The stability of internal solitary waves

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A new class of time discretization schemes for the solution of nonlinear PDEs

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Singularity formation in the generalized Benjamin-Ono equation

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Stability and instability of solitary waves of Korteweg-de Vries type

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Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions

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Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions

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Smoothing and dispersive estimates for 1D Schrödinger equations with BV coefficients and applications

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On well-posedness for the Benjamin-Ono equation

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Complete integrable particle methods and the recurrence of initial states for a nonlinear shallow-water wave equation

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A Complete Orthonormal System of Functions in $L^2 ( - \infty ,\infty )$ Space

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Exponential time differencing for stiff systems

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Numerical method satisfying the first two conservation laws for the Korteweg-de Vries equation

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Solitary internal waves in deep water

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A pseudo-spectral method for a non-local KdV-Burgers equation posed on $\mathbb{R}$

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Numerical simulation of focusing stochastic nonlinear Schrödinger equations

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Error Estimate of the Fourier Collocation Method for the Benjamin-Ono Equation

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Numerical approximation of solitary waves of the Benjamin equation

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Convergence of finite difference schemes for the Benjamin-Ono equation

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Global well-posedness for the $k$-dispersion generalized Benjamin-Ono equation.

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Q3446085

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Self-focusing in the damped nonlinear Schrödinger equation

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The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems

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Uniqueness of non-linear ground states for fractional Laplacians in $\mathbb{R}$

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A convergent Crank-Nicolson Galerkin scheme for the Benjamin-Ono equation

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Q3469579

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On Blow-up Solutions to the 3D Cubic Nonlinear Schrodinger Equation

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A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation

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Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation

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Global well-posedness of the Benjamin–Ono equation in low-regularity spaces

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On the cauchy problem for the benjamin-ono equation

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Models for internal waves in deep water

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Fourth-Order Time-Stepping for Stiff PDEs

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Complete integrability of the Benjamin-Ono equation by means of action-angle variables

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Perturbation theory for the Benjamin-Ono equation

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The Inverse Scattering Transform for the Benjamin–Ono Equation

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On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations

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Asymptotic stability of solitons for the Benjamin-Ono equation

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Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case

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On the Generalized Benjamin-Ono Equation

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Global wellposedness of the modified Benjamin-Ono equation with initial data in H1/2

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Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg-de Vries equations

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Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation

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Numerical study of Zakharov-Kuznetsov equations in two dimensions

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IST Versus PDE: A Comparative Study

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Q4808272

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Direct and inverse scattering problems of the nonlinear intermediate long wave equation

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Convergence of Petviashvili's Method near Periodic Waves in the Fractional Korteweg--de Vries Equation

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Focusing singularity in a derivative nonlinear Schrödinger equation

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Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation

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New Representations of Multiperiodic and Multisoliton Solutions for a Class of Nonlocal Soliton Equations

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An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations

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Internal wave solitons

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

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The Benjamin-Ono hierarchy with asymptotically reflectionless initial data in the zero-dispersion limit

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A note on the numerical and $N$-soliton solutions of the Benjamin-Ono evolution equation

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The Cauchy problem for the Benjamin-Ono equation in $L^{2}$ revisited

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Q4650700

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Well-posedness results for the generalized Benjamin-Ono equation with small initial data.

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A direct method of calculating periodic wave solutions to nonlinear evolution equations. I: Exact two-periodic wave solution

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Petviashvilli's method for the Dirichlet problem

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Algebraic solitary waves in stratified fluids

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Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations

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Bifurcations of new eigenvalues for the Benjamin–Ono equation

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Numerical solution of some nonlocal, nonlinear dispersive wave equations

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On the global well-posedness of the Benjamin-Ono equation

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On the IVP for the k-Generalized Benjamin–Ono Equation

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Sur quelques généralisations de l'équation de Korteweg-de Vries

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Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE

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On the development of a high-order compact scheme for exhibiting the switching and dissipative solution natures in the Camassa-Holm equation

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Q5490997

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GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H<sup>1</sup>(<b>R</b>)

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On the asymptotic behavior of large radial data for a focusing nonlinear Schrödinger equation

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A numerical method for the Benjamin-Ono equation

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Sharp well-posedness results for the generalized Benjamin-Ono equation with high nonlinearity.

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Well-posedness for the Generalized Benjamin–Ono Equations with Arbitrary Large Initial Data in the Critical Space

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Computing the Hilbert Transform on the Real Line

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Solitary waves of nonlinear dispersive evolution equations with critical power nonlinearities

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Jost Solutions and the Direct Scattering Problem of the Benjamin--Ono Equation

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2021.110570

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Sitelinks

Mathematics(1 entry)

mardi Publication:2133012