Eigenvalue cutoff in the cubic-quintic nonlinear Schrödinger equation.
Using theoretical arguments, we prove the numerically well-known fact that the eigenvalues of all localized stationary solutions of the cubic-quintic (2+1) -dimensional nonlinear Schrödinger equation exhibit an upper cutoff value. The existence of the cutoff is inferred using Gagliardo-Nirenberg and Hölder inequalities together with Pohozaev identities. We also show that, in the limit of eigenvalues close to zero, the eigenstates of the cubic-quintic nonlinear Schrödinger equation behave similarly to those of the cubic nonlinear Schrödinger equation.
Departamento de Matemáticas, E.T.S. Ingenieros Industriales and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha, Avenida Camilo José Cela 3, Ciudad Real, 13071 Spain.
Vladyslav
V
Prytula
Vadym
V
Vekslerchik
Víctor M
VM
Pérez-García