Nonlinear Analysis 63 (2005) e2197 – e2208 www.elsevier.com/locate/na The stability of the governing equation of envelope surface created by nearly bichromatic waves propagating on an elastic plate B.T. Nohara ∗, 1 , A. Arimoto Department of Electronic and Computer Engineering, Faculty of Engineering, Musashi Institute ofTechnology, Tamazutsumi, Setagaya, Tokyo 158-8557, Japan Abstract We study the stability of the governing equation of envelope surface created by nearly bichromatic waves propagating on an elastic plate. Nearly bichromatic waves are defined by the waves that almost concentrate the energy in two wavenumbers, which very closely approach each other. We present the solution of the governing equation for nearly bichromatic waves is stable.  2004 Elsevier Ltd. All rights reserved. Keywords: Elastic plate; Envelope; Nearly bichromatic waves; Nearly monochromatic waves; Schrödinger equation 1. Preliminaries We consider the propagating waves on an elastic plate [1,2] and in particular, study the stability of solutions of the following equation: i  A t +   ′ (k 0 ) +  ′′ (k 0 )  1 2 + i 2 (cosec(g(x,y,t)) - cot (g(x,y,t)))  ×  cos  0 A x + sin  0 A y  +  ′′ (k 0 ) 2   2 A x 2 +  2 A y 2  = 0, (1) ∗ Corresponding author. E-mail address: drben@ac.cs.musashi-tech.ac.jp (B.T. Nohara). 1 A part of this research is supported by the US Air Force Grant: AOARD-03-4047. 0362-546X/$ - see front matter  2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.na.2004.09.010