Construction of Partial Differential Equations with Conditional Symmetries

  • Decio LeviEmail author
  • Miguel A. Rodríguez
  • Zora Thomova
Part of the CRM Series in Mathematical Physics book series (CRM)


Nonlinear PDEs having given conditional symmetries are constructed. They are obtained starting from the invariants of the conditional symmetry generator and imposing the extra condition given by the characteristic of the symmetry. Series of examples of new equations, constructed starting from the conditional symmetries of Boussinesq, are presented and discussed thoroughly to show and clarify the methodology introduced.


Lie symmetries Partial differential equations Conditional symmetries Point transformations Boussinesq equation 



DL has been supported by INFN IS-CSN4 Mathematical Methods of Nonlinear Physics. DL thanks ZT and the SUNY Polytechnic Institute for their warm hospitality at Utica when this work was started. DL thanks the Departamento de Física Téorica of the Complutense University in Madrid for its hospitality. MAR was supported by the Spanish MINECO under project FIS 2015-63966-P. D. Nedza, summer student of ZT, contributed to the verification of some of the computations.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Decio Levi
    • 1
    Email author
  • Miguel A. Rodríguez
    • 2
  • Zora Thomova
    • 3
  1. 1.INFN, Sezione Roma TreRomaItaly
  2. 2.Dept. de Física TeóricaUniversidad Complutense de MadridMadridSpain
  3. 3.SUNY Polytechnic InstituteUticaUSA

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