KdVB方程行波解的定量分析
A Quantitative Analysis of the Travelling Wave Solution of the KdV-Burgers Equation
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摘要: 本文利用数学分析的方法、研究了v2≥4μ时KdVB方程的行波解.证明KdVB方程行波解与相应的Burgers方程行波解在定量方面的类似性.证明一般渐近展开式的截断误差是小参数ε的高阶量.Abstract: By using the methods of mathematics analysis, we investigate the travelling wave solution of the KdVB equation under the assumption v2≥4μ.We prove that the travelling wave solution is quantitatively similar to the corresponding Burgers shock wave. Then we prove that the absolute error of the general asymptotic expansion is high order quantity of the small parameter ε.
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Key words:
- KdVB equation /
- asymptotics /
- travelling wave
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[1] 吕咸青,KdVB方程行波解的渐近分析,物理学报,47 (2)(7992),177. [2] 管克英、高歌,Burgers-K-dV混合型方程行波解的定性分析,中国科学(A辑),(7) (7987),64. -
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