Notes on a high order fully discrete scheme for the Korteweg-de vries equation with a time-stepping procedure of Runge-Kutta-composition type

利用计算机编程求解Korteweg de Vries和Korteweg de Vries-Burger方程的数值解

Numerical solutions of Korteweg de Vries and Korteweg de Vries-Burger's equations using computer programming

本文采用sinc配点法数值求解KdV和KdVB方程，通过有限差分和θ加权格式离散时间与空间导数，利用Mathematica编程实现矩阵求解，并给出最大绝对误差和守恒律。

广义五阶Korteweg-de Vries方程族的无网格数值解

A meshless numerical solution of the family of generalized fifth-order Korteweg-de Vries equations

采用无网格线法，结合径向基函数空间离散和龙格-库塔时间积分，求解广义五阶KdV方程族，数值结果与精确解对比显示高精度。

一种用于广义Korteweg de-Vries方程的高阶IMEX方法

A High Order IMEX Method for Generalized Korteweg de-Vries Equations

针对广义Korteweg de-Vries方程，提出一种结合连续$H^1$-协调有限元空间离散与IMEX时间离散的高阶时空逼近方法，该方法稳定且保质量，通过理论证明与数值模拟验证了其有效性。

Spectral approach to Korteweg-de Vries equations on the compactified real line

We present a numerical approach for generalised Korteweg-de Vries (KdV) equations on the real line. In the spatial dimension we compactify the real line and apply a Chebyshev collocation method. The time integration is performed with an implicit Runge-Kutta method of fourth order. Several examples are discussed: initial data bounded but not vanishing at infinity as well as data not satisfying the Faddeev condition, i.e. with a slow decay towards infinity.

Solitary water wave interactions for the Forced Korteweg-de Vries equation

The aim of this work is to study solitary water wave interactions between two topographic obstacles for the forced Korteweg-de Vries equation (fKdV). Focusing on the details of the interactions, we identify regimes in which solitary wave interactions maintain two well separated crests and regimes where the number of local maxima varies according to the laws $2\rightarrow 1\rightarrow 2\rightarrow 1\rightarrow 2$ or $2\rightarrow 1\rightarrow 2$. It shows that the geometric Lax-categorization of Korteweg-de Vries (KdV) two-soliton interactions still holds for the fKdV equation.

随机演化方程的弱收敛速率及其在非线性随机波、HJMM、随机薛定谔和线性化随机科赫登-德维里斯方程中的应用

Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schrödinger and linearized stochastic Korteweg-de Vries equations

本文研究了广泛随机演化方程噪声离散化的弱收敛速率，针对非正则化半群和加性或乘性噪声，提出了一种方法，该方法在非线性随机波、HJMM、随机薛定谔和线性化随机科赫登-德维里斯方程中得到应用，并在重要方程中提供了最优收敛速率。