An integrable shallow water equation with linear and nonlinear dispersion.
An integrable shallow water equation with linear and nonlinear dispersion.
复制标题
DOI：
10.1103/physrevlett.87.194501
复制
发表时间：
2001-04
影响因子：
8.6
通讯作者：
H. Dullin;G. Gottwald;Darryl D. Holm
中科院分区：
文献类型：
--
作者：
H. Dullin;G. Gottwald;Darryl D. Holm
我们使用渐近分析和近单位正规形变换从水波理论导出1+1单向非线性波动方程，该方程结合了Korteweg-deVries（KdV）方程的线性色散和Camassa-Holm（CH）方程的非线性/非局部色散。该方程在超越KdV的渐近近似中更精确一阶，但通过逆散射变换方法仍然保持完全可积性。其行波解包含KdV孤子和CH峰作为极限情况。
We use asymptotic analysis and a near-identity normal form transformation from water wave theory to derive a 1+1 unidirectional nonlinear wave equation that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation. This equation is one order more accurate in asymptotic approximation beyond KdV, yet it still preserves complete integrability via the inverse scattering transform method. Its traveling wave solutions contain both the KdV solitons and the CH peakons as limiting cases.