Families of Solutions of Multitemporal Nonlinear Schrödinger PDE

Cristian Ghiu, Constantin Udriste and Lavinia Laura Petrescu
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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
Constantin Udriste: Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 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

Mathematics, 2021, vol. 9, issue 16, 1-24

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.

Keywords: multitime nonlinear Schrödinger PDE; oblique derivative; exact solutions; first integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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