Variational principles and conservation laws to the Burridge-Knopoff equation


Yasar E.

NONLINEAR DYNAMICS, vol.54, no.4, pp.307-312, 2008 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.1007/s11071-008-9330-x
  • Journal Name: NONLINEAR DYNAMICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.307-312
  • Keywords: Adjoint equation, Burridge-Knopoff equation, Conservation laws, Lagrangian, Nonlocal variables, Symmetries, SYMMETRIES

Abstract

We generate conservation laws for the Burridge-Knopoff equation which model nonlinear dynamics of earthquake faults by a new conservation theorem proposed recently by Ibragimov. One can employ this new general theorem for every differential equation (or systems) and derive new local and nonlocal conservation laws. Nonlocal conservation laws comprise nonlocal variables defined by the adjoint equations to the Burridge-Knopoff equation.