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Families of Solutions of Multitemporal Nonlinear Schrödinger PDE

Author

Listed:
  • Cristian Ghiu

    (Department of Mathematical Methods and Models, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania
    These authors contributed equally to this work.)

  • Constantin Udriste

    (Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania
    These authors contributed equally to this work.
    Second address: Academy of Romanian Scientists, Ilfov 3, Sector 5, RO-050044 Bucharest, Romania.)

  • Lavinia Laura Petrescu

    (Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

The multitemporal nonlinear Schrödinger PDE (with oblique derivative) was stated for the first time in our research group as a universal amplitude equation which can be derived via a multiple scaling analysis in order to describe slow modulations of the envelope of a spatially and temporarily oscillating wave packet in space and multitime (an equation which governs the dynamics of solitons through meta-materials). Now we exploit some hypotheses in order to find important explicit families of exact solutions in all dimensions for the multitime nonlinear Schrödinger PDE with a multitemporal directional derivative term. Using quite effective methods, we discovered families of ODEs and PDEs whose solutions generate solutions of multitime nonlinear Schrödinger PDE. Each new construction involves a relatively small amount of intermediate calculations.

Suggested Citation

  • Cristian Ghiu & Constantin Udriste & Lavinia Laura Petrescu, 2021. "Families of Solutions of Multitemporal Nonlinear Schrödinger PDE," Mathematics, MDPI, vol. 9(16), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1995-:d:618613
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