On the long time behaviour of a generalized KdV equation

✍ Scribed by A. Sidi; C. Sulem; P. L. Sulem

• Publisher: Springer Netherlands
• Year: 1986
• Tongue: English
• Weight: 495 KB
• Volume: 7
• Category: Article
• ISSN: 0167-8019
• DOI: 10.1007/bf00046976

✦ Synopsis

We consider the Cauchy problem for the generalized Korteweg-de Vries equation

~,u + O~(-O~)~u + a~( u----A ) = O

where ~ is a positive real and it an integer larger than 1. We obtain the detailed large distance behaviour of the fundamental solution of the linear problem and show that for ot/>12 and it > a + ~ + (a2+ 3a + 4~) 1/2, solutions of the nonlinear equation with small initial conditions are smooth in the large and asymptotic when t---~ ± oo to solutions of the linear problem. (1950). 35020, 35B40.

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