On the nonlinear stability of solitary wave solutions of the fifth-order Korteweg–de Vries equation

✍ Scribed by F. Dias; E.A. Kuznetsov

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 67 KB
• Volume: 263
• Category: Article
• ISSN: 0375-9601
• DOI: 10.1016/s0375-9601(99)00712-4

✦ Synopsis

For the fifth-order Korteweg-de Vries equation it is demonstrated that the Hamiltonian is bounded from below for fixed momentum. If there exists a solitary wave solution which realizes this minimum, then it is stable with respect to not only small perturbations but also finite ones. The proof is based on both the Lyapunov theorem and an integral estimation of the Sobolev-Gagliardo-Neirenberg inequalities.