文档介绍：Chaos, Solitons and Fractals 26 (2005) 1363–1375
ate/chaos
On the Painleve´ integrability, periodic wave solutions
and soliton solutions of generalized coupled
higher-order nonlinear Schro¨dinger equations
Gui-qiong Xu a,*, Zhi-bin Li b
a Department of Information Management, College of International Business and Management, Shanghai University,
Shanghai 201800, China
b Department puter Science, East China Normal University, Shanghai 200062, China
Accepted 31 March 2005
Abstract
It is proven that generalized coupled higher-order nonlinear Schro¨dinger equations possess the Painleve´ property for
two particular choices of parameters, using the Weiss–Tabor–Carnevale method and KruskalÕs simplification. Abun-
dant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with
the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright
soliton, dark soliton and mixed dark and bright soliton solutions with physical interests.
Ó 2005 Elsevier Ltd. All rights reserved.
1. Introduction
The nonlinear Schro¨dinger (NLS) equation, which describes the time evolution of a slowly varying envelope, has
many applications in various branches of physics. In deriving the NLS equation, higher-order terms have been ne-
glected under appropriate physical assumptions. With the recent developments in optical technology, higher-order cor-
rections to the NLS equation have e necessary and important. One of the higher-order NLS equations is
2 2 2
iU t þ U zz þ bjUj U À ikU zzz þ cjUj U z þ dðjUj ÞzU ¼ 0;
which models the dynamics of a nonlinear pulse envelope in a fiber [1]. The last term proportional to d es impor-
tant for short-pulse propagation over long distances.
To describe two pulses co-propagating in optical fibers, we need to consider a ponent generalization of the
ponent propagation equation [2–5]. For this purpose, we consider a generali