Mixed dispersion nonlinear Schrödinger equation in higher dimensions: theoretical analysis and numerical computations

In the present work we provide a characterization of ground states higher-dimensional quadratic-quartic model nonlinear Schr{\"o}dinger class with combination focusing biharmonic operator either an isotropic or anisotropic defocusing Laplacian (at linear level) and power-law nonlinearity. Examining principally prototypical example dimension $d=2$, find that instability arises beyond certain threshold coefficient between cubic quintic cases, while all solutions are stable for powers below cubic. Above quintic, up to critical nonlinearity exponent $p$, there exists progressively narrowing range frequencies. Finally, above $p$ unstable. The picture is rather similar in case, difference even before numerical computations suggest interval unstable Our analysis generalizes relevant observations arbitrary combinations prefactor $b$ power $p$.