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VOL. 14 | 2013 Symmetry Properties of the Membrane Shape Equation
Vladimir Pulov, Edy Chacarov, Mariana Hadzhilazova, Ivaïlo Mladenov

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka


Here we consider the Helfrich's membrane shape model from a group-theoretical viewpoint. By making use of the conformal metric on the associated surface the model is represented by a system of four second order nonlinear partial differential equations. In order to construct the determining system for the symmetries of the metric we rely on the previously developed package LieSymm-PDE within ${\tt Mathematica}^{\!®}$. In this way we have obtained the determining system consisting of 206 equations. Using the above mentioned programs we have solved the equations in a semi-automatic way. As a result we end up with an infinite dimensional symmetry Lie algebra of the Helfrich`s model in conformal metric representation which we present here in explicit form.


Published: 1 January 2013
First available in Project Euclid: 13 July 2015

zbMATH: 1382.35005
MathSciNet: MR3183937

Digital Object Identifier: 10.7546/giq-14-2013-152-159

Rights: Copyright © 2013 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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