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Variational approximation and the use of collective coordinates

Dawes, JHP and Susanto, H (2013) 'Variational approximation and the use of collective coordinates.' Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 87 (6). ISSN 1539-3755

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Abstract

We consider propagating, spatially localized waves in a class of equations that contain variational and nonvariational terms. The dynamics of the waves is analyzed through a collective coordinate approach. Motivated by the variational approximation, we show that there is a natural choice of projection onto collective variables for reducing the governing (nonlinear) partial differential equation (PDE) to coupled ordinary differential equations (ODEs). This projection produces ODEs whose solutions are exactly the stationary states of the effective Lagrangian that would be considered in applying the variational approximation method. We illustrate our approach by applying it to a modified Fisher equation for a traveling front, containing a non-constant-coefficient nonlinear term. We present numerical results that show that our proposed projection captures both the equilibria and the dynamics of the PDE much more closely than previously proposed projections. © 2013 American Physical Society.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 12 Nov 2014 19:41
Last Modified: 30 Jan 2019 16:18
URI: http://repository.essex.ac.uk/id/eprint/11553

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