On numerical approaches to nonlinear Schrödinger and Korteweg-de Vries equations for piecewise smooth and slowly decaying initial data

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Multidomain spectral method for Schrödinger equations
A method for numerical integration on an automatic computer
Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations
Low regularity exponential-type integrators for semilinear Schrödinger equations
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton
Multi-domain spectral approach for the Hilbert transform on the real line
Spectral approach to Korteweg-de Vries equations on the compactified real line
Numerical study of break-up in solutions to the dispersionless Kadomtsev-Petviashvili equation
Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis
A numerical approach to blow-up issues for dispersive perturbations of Burgers' equation
An exponential-type integrator for the KdV equation
Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations
Exponential integrators
The Exponentially Convergent Trapezoidal Rule
Fourth Order Time-Stepping for Kadomtsev–Petviashvili and Davey–Stewartson Equations
On the Product of Semi-Groups of Operators
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
Spectral Methods in MATLAB
Computing the Dynamics of Complex Singularities of Nonlinear PDEs
On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
Fourth-Order Time-Stepping for Stiff PDEs
Numerical study of fractional nonlinear Schrödinger equations
Is Gauss Quadrature Better than Clenshaw–Curtis?
On the Construction and Comparison of Difference Schemes
Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

This page was built for publication: On numerical approaches to nonlinear Schrödinger and Korteweg-de Vries equations for piecewise smooth and slowly decaying initial data