Optical collapse is a fascinating research topic. The propagation of intense laser beams in a
transparent medium is usually modeled by the two-dimensional nonlinear Schrödinger …

In this paper, we study the existence of solutions to the mixed dispersion nonlinear
Schrödinger equation\[\gamma\Delta^ 2 u-\Delta u+\alpha u=| u|^{2\sigma} u,\qquad u\in H …

A.–We consider the Cauchy problem for the biharmonic (ie, fourth-order) NLS
with focusing nonlinearity given by i@ tu D 2u u juj2 u for. t; x/2 Œ0; T/Rd; where 0<< 1 for …

We study the local and global wellposedness of the initial-boundary value problem for the
biharmonic Schr\" odinger equation on the half-line with inhomogeneous Dirichlet-Neumann …

We prove scattering for the defocusing fourth-order Schrödinger equation in low spatial
dimensions (1⩽ n⩽ 4). Inspired by the method in (Pausader 2010 Indiana Univ. Math. J. 59 …

In this note, we prove the instability by blow-up of the ground state solutions for a class of
fourth order Schrödinger equations. This extends the first rigorous results on blowing-up …

Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations
Page 1 Nonlinearity PAPER Dynamics of radial solutions for the focusing fourth-order …

We study the effect of a fourth-order derivative term in the diffusion of Brownian particles
confined to a narrow 2D channel whose longitudinal coordinate is larger than the …

In this paper, we study the ground state standing wave solutions for the focusing bi-harmonic
nonlinear Schrödinger equation with a μ-Laplacian term (BNLS). Such BNLS models the …

We revisit the finite time blow-up for the fourth-order Schrödinger equation with focusing
inhomogeneous nonlinearity−| x|− 2| u| 4 n u. By exploiting localized virial estimates and …