Non-linear Schrödinger Equation on Discrete Graphs

Akduman S., Karakılıç S.

European Women in Math. General Meeting 2022, Helsinki, Finlandiya, 22 - 26 Ağustos 2022, ss.3

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Helsinki
  • Basıldığı Ülke: Finlandiya
  • Sayfa Sayıları: ss.3
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

The nonlinear Schrödinger equation with growing potential has been extensively studied by both mathematicians and physicists from the fundamental well-posedness of Cauchy problem to the existence and stability of standing waves.
In this talk, we deal with NLS equation on discrete graphs assuming the linear potential is discrete. Making use of the generalized Nehari manifold approach, we prove the existence and multiplicity of standing waves for both self-focusing and defocusing cases. Our approach is variational and based on the critical point theory applied to the energy functional restricted to the generalized Nehari manifold. This is a joint work with Sedef Karakılıc (Dokuz Eylul University).