Eur. Phys. J. B (2013) 86: 217
https://doi.org/10.1140/epjb/e2013-31120-7

Regular Article

Solitary waves of α-helix propagation in media with arbitrary inhomogeneities

¹ Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
² Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
³ Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

^a e-mail: mvogal2009@yahoo.fr

Received: 12 December 2012
Received in final form: 14 March 2013
Published online: 16 May 2013

Abstract

We study the dynamics of solitary waves in α-helical proteins going beyond the standard nearest-neighbour interaction by taking into account influence long-range dipole-dipole interactions of the Kac-Baker type. By means of the coherent state representation of operators, the model Hamiltonian is transformed into a pair of classical lattice equations, which is further reduced to a sole nonlinear Schrödinger (NLS) equation using the continuum approximation of which the dispersive coefficient depends on the long-range interactions (LRI) parameter. It comes out from our results that the bright-like solitons, solitary waves which govern the energy transfer in α-helix, are deeply influenced by the LRI. At the end, we transform the NLS equation for more currently-important inhomogeneous NLS models in media with inhomogeneities. Application of this transformation to two example models is illustrated and soliton-like solutions are also graphically discussed.