Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study
DOI10.1016/j.jcp.2021.110570OpenAlexW3111829784MaRDI QIDQ2133012
Zhongming Wang, Svetlana Roudenko, Kai Yang
Publication date: 29 April 2022
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.03336
[https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DNumerical+methods+for+partial+differential+equations%2C+initial+value+and+time-dependent+initial-boundary+value+problems%26go%3DGo Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)] [https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DPartial+differential+equations+of+mathematical+physics+and+other+areas+of+application%26go%3DGo Partial differential equations of mathematical physics and other areas of application (35Qxx)] [https%3A%2F%2Fportal.mardi4nfdi.de%2Fw%2Findex.php%3Ftitle%3D%2BSpecial%253ASearch%26search%3DIncompressible+inviscid+fluids%26go%3DGo Incompressible inviscid fluids (76Bxx)]
Related Items (5)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Petviashvilli's method for the Dirichlet problem
- Convergence of finite difference schemes for the Benjamin-Ono equation
- The Benjamin-Ono hierarchy with asymptotically reflectionless initial data in the zero-dispersion limit
- Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
- Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions
- On the development of a high-order compact scheme for exhibiting the switching and dissipative solution natures in the Camassa-Holm equation
- On the asymptotic behavior of large radial data for a focusing nonlinear Schrödinger equation
- Sharp well-posedness results for the generalized Benjamin-Ono equation with high nonlinearity.
- Exponential time differencing for stiff systems
- On the global well-posedness of the Benjamin-Ono equation
- Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
- Nonlocal models for nonlinear, dispersive waves
- Complete integrable particle methods and the recurrence of initial states for a nonlinear shallow-water wave equation
- An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations
- Sufficient conditions for stability of solitary-wave solutions of model equations for long waves
- Solitary waves of nonlinear dispersive evolution equations with critical power nonlinearities
- Sur quelques généralisations de l'équation de Korteweg-de Vries
- Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane
- A note on the numerical and \(N\)-soliton solutions of the Benjamin-Ono evolution equation
- A numerical method for the Benjamin-Ono equation
- A new class of time discretization schemes for the solution of nonlinear PDEs
- On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations
- Well-posedness results for the generalized Benjamin-Ono equation with small initial data.
- Models for internal waves in deep water
- Numerical solution of some nonlocal, nonlinear dispersive wave equations
- A convergent Crank-Nicolson Galerkin scheme for the Benjamin-Ono equation
- Singularity formation in the generalized Benjamin-Ono equation
- 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
- Numerical study of Zakharov-Kuznetsov equations in two dimensions
- Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation
- Focusing singularity in a derivative nonlinear Schrödinger equation
- Numerical approximation of solitary waves of the Benjamin equation
- Global well-posedness for the \(k\)-dispersion generalized Benjamin-Ono equation.
- Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg-de Vries equations
- Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions
- A pseudo-spectral method for a non-local KdV-Burgers equation posed on \(\mathbb{R}\)
- Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation
- Numerical method satisfying the first two conservation laws for the Korteweg-de Vries equation
- On well-posedness for the Benjamin-Ono equation
- Smoothing and dispersive estimates for 1D Schrödinger equations with BV coefficients and applications
- A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation
- Asymptotic stability of solitons for the Benjamin-Ono equation
- Self-Focusing in the Damped Nonlinear Schrödinger Equation
- IST Versus PDE: A Comparative Study
- Algebraic Solitary Waves in Stratified Fluids
- A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution
- On the zero-dispersion limit of the benjamin-ono cauchy problem for positive initial data
- Scaling, stability and singularities for nonlinear, dispersive wave equations: the critical case
- Well-posedness for the Generalized Benjamin–Ono Equations with Arbitrary Large Initial Data in the Critical Space
- Global wellposedness of the modified Benjamin-Ono equation with initial data in H1/2
- Global well-posedness of the Benjamin–Ono equation in low-regularity spaces
- Error Estimate of the Fourier Collocation Method for the Benjamin-Ono Equation
- The stability of internal solitary waves
- On the cauchy problem for the benjamin-ono equation
- Stability and instability of solitary waves of Korteweg-de Vries type
- Direct and inverse scattering problems of the nonlinear intermediate long wave equation
- Internal wave solitons
- Perturbation theory for the Benjamin-Ono equation
- On the Generalized Benjamin-Ono Equation
- Model equations for waves in stratified fluids
- GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H1(R)
- On the IVP for the k-Generalized Benjamin–Ono Equation
- Jost Solutions and the Direct Scattering Problem of the Benjamin--Ono Equation
- Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations
- New Representations of Multiperiodic and Multisoliton Solutions for a Class of Nonlocal Soliton Equations
- Bifurcations of new eigenvalues for the Benjamin–Ono equation
- The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
- The Inverse Scattering Transform for the Benjamin–Ono Equation
- Computing the Hilbert Transform on the Real Line
- Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation
- Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE
- A Complete Orthonormal System of Functions in $L^2 ( - \infty ,\infty )$ Space
- Convergence of Petviashvili's Method near Periodic Waves in the Fractional Korteweg--de Vries Equation
- Fourth-Order Time-Stepping for Stiff PDEs
- On Blow-up Solutions to the 3D Cubic Nonlinear Schrodinger Equation
- Internal waves of permanent form in fluids of great depth
- Solitary internal waves in deep water
- Numerical simulation of focusing stochastic nonlinear Schrödinger equations
This page was built for publication: Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study