Exact Theory of Solitary Waves in a Stratified Fluid with Surface Tension. Part I. Nonoscillatory Case

✍ Scribed by S.M. Sun; M.C. Shen

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 564 KB
• Volume: 105
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1993.1084

✦ Synopsis

In this paper we study steady permanent waves in a stratified fluid with surface tension over a flat horizontal bottom. We show that there exists a solitary wave solution of the exact equations, which decays to zero at infinity, if the linearized equations possess no positive eigenvalues. In contrast to the classical case of a fluid with constant density, there are infinitely many critical values (\tau_{c n}) of the Bond number (\tau), and positive eigenvalues of the linearized equations may appear for both (\tau>\tau_{c n}) and (\tau<\tau_{c n}). A positive eigenvalues may cause small-amplitude oscillations and the oscillatory case will be treated in Part II. 1993 Academic Press. Inc.