KdVB方程行波解的渐近分析

AN ASYMPTOTIC ANALYSIS OF THE TRAVELLING WAVE SOLUTION OF THE KdV BURGERS EQUATION

本文利用奇异摄动的理论和方法,研究v^2》4μ时KdVB方程的行波解,得到行波解的三阶渐近展开式的显式,同时得到行波解的一般渐近展开式的表达式:u≈u^(0)+8u^(1)+8~1u^(2)+…+8~nu^(n)+…;并且证明u^(j)(j=1,2,…,n,…)都是有界函数。

By applying the theory and method of singular perturbations, we investigate the travelling wave solution of the KdVB equation under the assumption v2》4μ. We get the explicit expression of the travelling wave solution up to the third order at first. Then, we obtain the general asymptotic expansion: u = u(0)+εu(1)+ε2u(2)+…+ εnu(n) + …?and prove that u(i)(j=1,2,…,n,…) are bounded functions.