Application of the extended Lie group analysis to the Hopf functional formulation of the Burgers equation

Marta Wacławczyk, Martin Oberlack

Journal of Mathematical Physics

54, 2013, 072901, 10.1063/1.4812803

A study concerning the Lie group analysis of the functional differential equations has been performed. This is a continuation of the previous common work of Oberlack and Waclawczyk ["On the extension of Lie group analysis to functional differential equations," Arch. Mech. 58, 597 (2006)] where Lie group theory has been extended to functional differential equations and a special solution of the functional formulation of the Burgers equation was derived based on the calculated set of infinitesimals. Here we derive an infinite set of symmetry transformations of this equation and find new and more general invariant solutions. With this we get a step closer to solutions of functional differential equations, which, e. g., give a complete statistical description of turbulence in case of the famous Hopf-Novikov-Stokes functional differential equations. (C) 2013 AIP Publishing LLC.