𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Interaction Equations for Short and Long Dispersive Waves

✍ Scribed by Daniella Bekiranov; Takayoshi Ogawa; Gustavo Ponce

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
380 KB
Volume
158
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

dedicated to professor rentaro agemi on his sixtieth birthday

We show the time-local well-posedness for a system of nonlinear dispersive equations for the water wave interaction

It is shown that for any initial data (u 0 , v 0 ) # H s (R)_H s&1Γ‚2 (R) (s 0), the solution for the above equation uniquely exists in a subset of C((&T, T); H s )_ C((&T, T); H s&1Γ‚2 ) and depends continuously on the data. By virtue of a special structure of the nonlinear coupling, the solution is stable under a singular limiting process.

πŸ“œ SIMILAR VOLUMES

Orbital stability of solitary waves of t
Orbital stability of solitary waves of the long wave–short wave resonance equations
✍ Boling Guo; Lin Chen πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 117 KB

## Communicated by B. Brosowski This paper concerns the orbital stability for solitary waves of the ΒΈong ΒΌave-Short ΒΌave resonance equations. Since the abstract results of Grillakis et al. [7,8] cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral a

Blowup phenomena for a new periodic nonl
Blowup phenomena for a new periodic nonlinearly dispersive wave equation
✍ Qiaoyi Hu; Zhaoyang Yin πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 136 KB πŸ‘ 1 views

## Abstract We first establish the local well‐posedness for a new periodic nonlinearly dispersive wave equation. We then present a precise blowup scenario and several blowup results of strong solutions to the equation. The obtained blowup results on the equation improve considerably recent results

Unique continuation for the symmetric re
Unique continuation for the symmetric regularized long wave equation
✍ Yadong Shang πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 153 KB

## Abstract The unique continuation property has been intensively studied for a long time due to the important role that plays in the applications. The validity of the unique continuation property for symmetric regularized long wave equation is showed in this paper. The result is established by usi