Scattering for the non-radial inhomogenous biharmonic NLS equation

Scattering for the Non-radial 3d Cubic Nonlinear Schrödinger Equation

Scattering of radial H solutions to the 3D focusing cubic nonlinear Schrödinger equation below a mass-energy threshold M [u]E[u] < M [Q]E[Q] and satisfying an initial mass-gradient bound ‖u0‖L2‖∇u0‖L2 < ‖Q‖L2‖∇Q‖L2 , where Q is the ground state, was established in Holmer-Roudenko [8]. In this note, we extend the result in [8] to non-radial H data. For this, we prove a non-radial profile decompo...

Enclosure for the Biharmonic Equation

In this paper we give an enclosure for the solution of the biharmonic problem and also for its gradient and Laplacian in the L2-norm, respectively.

Darboux transformation for the NLS equation

We analyze a certain class of integral equations associated with Marchenko equations and Gel’fand-Levitan equations. Such integral equations arise through a Fourier transformation on various ordinary differential equations involving a spectral parameter. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution in terms of the unper...

Efficient parallel solvers for the biharmonic equation

Fast Multipole Method for the Biharmonic Equation

The evaluation of sums (matrix-vector products) of the solutions of the three-dimensional biharmonic equation can be accelerated using the fast multipole method, while memory requirements can also be significantly reduced. We develop a complete translation theory for these equations. It is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering ...