Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 08, pp. 1-9.

Title: The Cauchy problem for a short-wave equation
   
Authors: Silvio Marques A. Gama (Univ. do Porto, Portugal)
         Gueorgui Smirnov       (Univ. do Porto, Portugal)

Abstract:
 We prove existence and uniqueness of solutions for the
 Cauchy problem of the simplest nonlinear short-wave equation,
 $u_{tx}=u-3u^{2}$,  with periodic boundary condition.
 
Submitted July 18, 2008. Published January 06, 2009.
Math Subject Classifications: 34A12, 34A34, 35Q35, 35Q53.
Key Words: Cauchy problem; Benjamin-Bona-Mahony-Perigrine equation;
           short-waves.