Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Physica D 176 (2003) 4466 Exact soliton solutions of the one-dimensional
 

Summary: Physica D 176 (2003) 44­66
Exact soliton solutions of the one-dimensional
complex Swift­Hohenberg equation
Ken-ichi Marunoa,b,, Adrian Ankiewiczc, Nail Akhmedievb
a Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
b Optical Sciences Centre, Research School of Physical Sciences and Engineering,
The Australian National University, Canberra ACT 0200, Australia
c Applied Photonics Group, Research School of Physical Sciences and Engineering,
The Australian National University, Canberra ACT 0200, Australia
Received 9 May 2002; received in revised form 1 October 2002; accepted 2 October 2002
Communicated by I. Gabitov
Abstract
Using Painlevé analysis, the Hirota multi-linear method and a direct ansatz technique, we study analytic solutions of the
(1 + 1)-dimensional complex cubic and quintic Swift­Hohenberg equations. We consider both standard and generalized
versions of these equations. We have found that a number of exact solutions exist to each of these equations, provided that the
coefficients are constrained by certain relations. The set of solutions include particular types of solitary wave solutions, hole
(dark soliton) solutions and periodic solutions in terms of elliptic Jacobi functions and the Weierstrass function. Although
these solutions represent only a small subset of the large variety of possible solutions admitted by the complex cubic and
quintic Swift­Hohenberg equations, those presented here are the first examples of exact analytic solutions found thus far.
© 2002 Elsevier Science B.V. All rights reserved.

  

Source: Akhmediev, Nail - Research School of Physical Sciences and Engineering, Australian National University
Australian National University, Research School of Physical Sciences and Engineering, Optical Sciences Group

 

Collections: Engineering; Physics