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Symmetry and Chaos in Differential Equations: Analytical and Numerical Methods with Applications

Call for Papers

Symmetry methods in differential equations (also known as Lie group analysis) provide a rigorous way to classify them according to their invariance properties. This allows us to obtain group invariant and partially invariant solutions of differential equations in a tractable manner. Conserved quantity is a natural consequence of the symmetry (Noether's theorem). Recent years have witnessed possible extensions of Lie's and Noether's results. We now know that integrable equations admit infinite number of symmetries (via recursion operator). Stimulated theory (dimensional analysis) stems from the symmetries of the governing equations. Last but not least symmetry methods can serve as efficient tools to study analytically the order in differential equations.

Breakdown of the symmetries leads to chaos in deterministic differential equations via various mechanisms such as period doubling and intermittency routes, torus breakdown, and separatrix splitting. Nonlinearity favours the numerical methods to study the disorder induced by chaos. Stochasticity observed in chaos is different than the one which appears in stochastic systems. This opens a new door to symmetry analysis of stochastic systems.

Original research articles as well as review articles that will stimulate the ongoing research are all welcome. Potential topics include, but are not limited to:

  • Recent developments in symmetry methods for deterministic differential equations
  • Recent developments in integrability of deterministic
  • Differential equations via symmetry methods
  • Advances in symmetry methods for stochastic
  • Differential equations
  • Analytical and numerical methods for chaotic deterministic systems
  • Recent advances in integrability of stochastic differential Equations

Before submission authors should carefully read over the journal's Author Guidelines, which are located at Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at according to the following timetable:

Manuscript DueFriday, 14 December 2012
First Round of ReviewsFriday, 8 March 2013
Publication DateFriday, 3 May 2013

Lead Guest Editor

  • Gazanfer ünal, Department of International Finance, Yeditepe University, Kayışdağı Ataşehir, Istanbul, Turkey

Guest Editors

  • Fazal M. Mahomed, Department of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa
  • Elhadj Zeraoulia, Department of Mathematics and Computer Sciences, University of Tébessa, Tébessa, Algeria