Non-linear phenomena in continuous media

last updated: December 2014


  • Dynamics of solitons and whirls in plasma, super fluid media, and BEC. 
  • Search for integrals and soliton solutions of non-linear physical effects.
  • Propagation of strong pulses through two-component plasmas.
  • Generalization of the WKB method. 
  • Application of non-linear equations to street traffic problems!   


  • Non-linear differential equations describing vehicle traffic on a highway (the Lighthill-Whitham-Payne model).
  • Predictions given by the developed two-particle two-parameter correlation function were compared with data obtained in two experiments run in Institute d'Optique (Palaiseau, France).
  • General form of boson separable quantum state density matrix was found and applied to investigate the dfk general properties of separable states.
  • Surfaces describing the CPN¾¾1 integrable complex projection models were investigated. General solutions of equations describing the projection operators of those models were sought for.  


  • QCD chiral condensate on temperature dependency was calculated in the Hadron Resonance Gas approximation. Hadron mass on quark mass dependency is an element of that theory. Various models including chiral perturbation theory and holographic theory were considered.
  • Lighthill-Whitham-Payne equations on stream density and velocity vs. x, t are very similar to equations describing a couple of different problems in physics. Successful integration of those equations is important for our view of other equations not solvable using traditional methods.
  • A simple relation between dfk and entanglement for bosons was shown. From the general form of the separable quantum state density matrix we have derived some inequalities which need to be met by the two-particle correlation function for the states. Experimental violation of the inequalities proves entanglement of the investigated quantum state.


  • Strict solutions obtained at some boundary conditions may find applications in solving some street traffic-related problems.
  • WKB method generalization is important for numerous fields of physics
  • The developed theory helps to understand and to estimate magnitude of the two-particle correlation function in the investigated system. The result may have important implications for several experiments. 


  • Professor  Eryk Infeld
  • Dr. Piotr Goldstein
  • Dr. Andrzej Skorupski
  • Dr. Paweł Zin
  • Dr. Maciej Pylak

This page edited by: Marek Pawłowski