Eigenvalue cutoff in the cubic-quintic nonlinear Schrodinger 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 Schrodinger equation exhibit an upper cutoff value. The existence of the cutoff is inferred using Gagliardo-Nirenberg and Holder inequalities together with Pohozaev identities. We also show that, in the limit of eigenvalues close to zero, the eigenstates of the cubic-quintic nonlinear Schrodinger equation behave similarly to those of the cubic nonlinear Schrodinger equation.