Nonlinear vector waves of a flexural mode in a chain model of atomic particles

Nikitenkova, S. P. and Raj, N. and Stepanyants, Y. A. (2015) Nonlinear vector waves of a flexural mode in a chain model of atomic particles. Communications in Nonlinear Science and Numerical Simulation, 20 (3). pp. 731-742. ISSN 1007-5704

Abstract

Flexural transverse waves in an anharmonic chain of atoms is considered and the nonlinear vector equation for the phonon modes in the long-wave approximation is derived taking into account the weak dispersion effects. Particular cases of the equation derived are discussed; among them the vector mKdV equation (Gorbacheva & Ostrovsky, 1983), as well as the new model vector equations dubbed here the 'second order cubic Benjamin–Ono (socBO) equation' and 'nonlinear pseudo-diffusion equation'. Stationary solutions to the equation derived are studied and it is found in which cases physically reasonable periodic and solitary type solutions may exist. The simplest non-stationary interactions of solitary waves of different polarisation are studied by means of numerical simulation. A new interesting phenomenon is revealed when two solitons of the same or opposite polarities interact elastically, whereas the interaction of two solitons lying initially in the perpendicular planes is essentially inelastic resulting in the survival of only one soliton and destruction of another one.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to published version due to publisher copyright policy.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 30 Sep 2014 21:06
Last Modified: 04 Apr 2017 04:49
Uncontrolled Keywords: chain model; particle interaction; nonlinear wave; kink; flexural mode; vector equation; mKdV equation; soliton interaction; stationary solution
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
02 Physical Sciences > 0203 Classical Physics > 020301 Acoustics and Acoustical Devices; Waves
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1016/j.cnsns.2014.05.031
URI: http://eprints.usq.edu.au/id/eprint/25944

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