KdVB方程行波解的渐近分析

本文利用奇异摄动的理论和方法,研究v²?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⁾+εu⁽¹⁾+ε¹u⁽²⁾+…+εⁿu⁽ⁿ⁾+…;并且证明u^(j)(j=1,2,…,n,…)都是有界函数。 关键词：

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

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 atfirst. Then, we obtain the general asymptotic expansion: u=u⁽⁰⁾+εu⁽¹⁾+ε¹u⁽²⁾+…+εⁿu⁽ⁿ⁾+… and prove that u^(j)(j=1,2,…,n,…) are bounded functions.
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