112 citations · 725 across the 43 of their papers we have counts for
31 papers · 1 filter
Numerical study of transverse (in-)stability of solitary waves in the cubic-quintic nonlinear Schrödinger equation
Christian Klein, Christof Sparber
We study the nonlinear Schrödinger equation with a competing cubic-quintic power law nonlinearity on the waveguide domain . This model is global…
Numerical evidence for singularity formation in defocusing fractional NLS in one space dimension
Christian Klein, Christof Sparber
We consider nonlinear dispersive equations of Schrödinger-type involving fractional powers of the Laplacian and a defocusing power-law nonlinearity. We conduct numerical…
Semiclassical wave-packets for weakly nonlinear Schrödinger equations with rotation
Xiaoan Shen, Christof Sparber
We consider semiclassically scaled, weakly nonlinear Schrödinger equations with external confining potentials and additional angular-momentum rotation term. This type of model aris…
Nonlinear bound states with prescribed angular momentum
Irina Nenciu, Xiaoan Shen, Christof Sparber
We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schrödinger equations with super-quadratic confinement in two and three spatial dimensions.…
Self-Bound vortex states in nonlinear Schrödinger equations with LHY correction
Anudeep K. Arora, Christof Sparber
We study the cubic-quartic nonlinear Schrödinger equation (NLS) in two and three spatial dimension. This equation arises in the mean-field description of Bose-Einstein condensates…
On soliton (in-)stability in multi-dimensional cubic-quintic nonlinear Schrödinger equations
R. Carles, C. Klein, C. Sparber
We consider the nonlinear Schrödinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The core of this article is the notion…
On an intercritical log-modified nonlinear Schrodinger equation in two spatial dimensions
Rémi Carles, Christof Sparber
We consider a dispersive equation of Schr{ö}dinger type with a non-linearity slightly larger than cubic by a logarithmic factor. This equation is supposed to be an effective model…
Orbital stability vs. scattering in the cubic-quintic Schrodinger equation
Rémi Carles, Christof Sparber
We consider the cubic-quintic nonlinear Schr{ö}dinger equation in space dimension up to three. The cubic nonlinearity is thereby focusing while the quintic one is defocusing, ensur…
On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates
Paolo Antonelli, Peter Markowich, Ryan Obermeyer +2
We study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a…
Stability and instability properties of rotating Bose-Einstein condensates
Jack Arbunich, Irina Nenciu, Christof Sparber
We consider the mean-field dynamics of Bose-Einstein condensates in rotating harmonic traps and establish several stability and instability properties for the corresponding solutio…
On a class of derivative Nonlinear Schrödinger-type equations in two spatial dimensions
J. Arbunich, C. Klein, C. Sparber
We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schrö…
Regularizing nonlinear Schroedinger equations through partial off-axis variations
Paolo Antonelli, Jack Arbunich, Christof Sparber
We study a class of focusing nonlinear Schroedinger-type equations derived recently by Dumas, Lannes and Szeftel within the mathematical description of high intensity laser beams […
Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement
Florian Mehats, Christof Sparber
We consider the three-dimensional time-dependent Gross-Pitaevskii equation arising in the description of rotating Bose-Einstein condensates and study the corresponding scaling limi…
Global attractor for a Ginzburg-Landau type model of rotating Bose-Einstein condensates
Alexey Cheskidov, Daniel Marahrens, Christof Sparber
We study the long time behavior of solutions to a nonlinear partial differential equation arising in the description of trapped rotating Bose-Einstein condensates. The equation can…
On the classical limit of a time-dependent self-consistent field system: analysis and computation
Shi Jin, Christof Sparber, Zhennan Zhou
We consider a coupled system of Schrödinger equations, arising in quantum mechanics via the so-called time-dependent self-consistent field method. Using Wigner transformation techn…
Numerical study of fractional Nonlinear Schrödinger equations
C. Klein, C. Sparber, P. Markowich
Using a Fourier spectral method, we provide a detailed numerically investigation of dispersive Schrödinger type equations involving a fractional Laplacian. By an appropriate choice…
Dispersive blow up for nonlinear Schroedinger equations revisited
Jerry L. Bona, Jean-Claude Saut, Gustavo Ponce +1
The possibility of finite-time, dispersive blow up for nonlinear equations of Schroedinger type is revisited. This mathematical phenomena is one of the possible explanations for oc…
On nonlinear Schrodinger type equations with nonlinear damping
Paolo Antonelli, Rémi Carles, Christof Sparber
We consider equations of nonlinear Schrodinger type augmented by nonlinear damping terms. We show that nonlinear damping prevents finite time blow-up in several situations, which w…
Well-Posedness and averaging of NLS with time-periodic dispersion management
Paolo Antonelli, Jean-Claude Saut, Christof Sparber
We consider the Cauchy problem for dispersion managed nonlinear Schroedinger equations, where the dispersion map is assumed to be periodic and piecewise constant in time. We establ…
Transverse stability of periodic traveling waves in Kadomtsev-Petviashvili equations: A numerical study
C. Klein, C. Sparber
We numerically investigate transverse stability and instability of so-called cnoidal waves, i.e., periodic traveling wave solutions of the Korteweg-de Vries equation, under the tim…
The Wigner-Fokker-Planck equation: Stationary states and large-time behavior
Anton Arnold, Irene M. Gamba, Maria Pia Gualdani +3
We consider the linear Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of per…
On the Cauchy Problem for nonlinear Schrödinger equations with rotation
Paolo Antonelli, Daniel Marahrens, Christof Sparber
We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. Thi…
Thermal effects in gravitational Hartree systems
Gonca L. Aki, Jean Dolbeault, Christof Sparber
We consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb-Newton interaction. For a given mass, we construct stationary states with non…
Geometric optics and instability for NLS and Davey-Stewartson models
Rémi Carles, Eric Dumas, Christof Sparber
We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrodinger equations with gauge invariant power-law nonlinearities and non-loca…