A note on the analytical solution to the modified perturbed Korteweg–de Vries equation Hilmi Demiray Faculty of Science and Letters, Department of Mathematics, Isik University, Buyukdere Caddesi 80670, Maslak-Istanbul, Turkey Abstract Motivated with a solitary wave type of solution to modified Korteweg–de Vries (KdV) equation, in this work we shall seek a travelling wave solution to the modified perturbed KdV equation. It is observed that the modified perturbed KdV equation still assumes a solitary wave solution with decaying amplitude in time. Ó 2002 Elsevier Science Inc. All rights reserved. Keywords: Modified KdV equation; Progressive waves 1. Travelling wave solution As is well known, various physical phenomena in engineering and physics may be described by some nonlinear differential equations. In order to get some information about the physical systems the exact or approximate solution of these equations must be given [1,2], but the solution methods are quite few and have some limitations. The inverse scattering method [3,4] and Hirota method [5] are two successful methods, but in some cases, either they are not sufficient or require quite involved calculations. In many physical systems, e.g., the differential equations governing the motion of a viscous fluid contained in an elastic tube [6], which are nonlinear, dispersive and dissipative the asymptotic analysis of the governing differential E-mail address: demiray@isikun.edu.tr (H. Demiray). 0096-3003/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII:S0096-3003(01)00297-1 Applied Mathematics and Computation 134 (2003) 501–505 www.elsevier.com/locate/amc