KdV孤波解的稳定性

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Stability of the Korteweg-de Vries Solitary Wave Solution

摘要: 本文探讨了KdV孤波解在无穷小扰动下的稳定性,证明KdV孤波解在李亚普诺夫意义下是不稳定的.
- KdV孤波解 /
- 不稳定 /
- 无穷小扰动 /
- 李亚普诺夫直接方法
Abstract: This paper considers the stabilily of the Korteweg-de Vries solitary wave solutionwith respect to infinitesmal dislurbance.It is found that the Korteweg-de Vries solitarywave solulion is unstable in the Liapunov sense.
- Korteweg-de Vries solitary wave solution /
- unstable /
- infinitesmal disturbance /
- Liapunov direct method

[1]	Jeffrey Alan and Tsunehiko Kakutani,Stability of the Burgers shock wave and the Korteweg de-Vries solution,Indiana UniversiW Mathematics,20,5(1970),463-468.
[2]	Jeffrey,Alan and Tsunehiko Kakutani,Weak nonlinear dispersive waves:A discussion centered around the korteweg-de vries equation,SIAM Rev.,14(1972),582-643.
[3]	廖晓听,《稳定性的数学理论及应用》.华中师范大学出版社(1988).57-59.