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Validity and dynamics in the nonlinearly excited 6th-order phase equation

Pages: 719 - 728, Issue special, November 2013

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Dmitry Strunin - University of Southern Queensland, Toowoomba, Queensland 4350, Australia (email)
Mayada Mohammed - University of Southern Queensland, Toowoomba, Queensland 4350, Australia (email)

Abstract: A slowly varying phase of oscillators coupled by diffusion is generally described by a partial differential equation comprising infinitely many terms. We consider a particular case when the coupling is nonlocal and, as a result, the equation can be reduced to a finite form with nonlinear excitation and 6th-order dissipation. We fulfilled two tasks: (1) evaluated the range of independent parameters rendering the form valid, and (2) developed and tested the numerical code for solving the equation; some numerical solutions are presented.

Keywords:  Partial differential equation, nonlinear excitation, dissipation.
Mathematics Subject Classification:  Primary: 35K55; Secondary: 65M06.

Received: September 2012; Published: November 2013.

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