The higher grading structure of the WKI hierarchy and the two-component short pulse equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Collective Perspective on Advances in Dyson-Schwinger Equation QCD

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evolution equation for short surface waves on water of finite depth

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical approximation of the Ginzburg-Landau equation with memory effects in the dynamics of phase transitions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

BCS-BEC crossover in a trapped Fermi super-fluid using a density-functional equation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Patch-size and isolation effects in the Fisher-Kolmogorov equation

We examine the classical problem of the existence of a threshold size for a patch to allow for survival of a given population in the case where the patch is not completely isolated. The surrounding habitat matrix is characterized by a non-zero carrying capacity. We show that a critical patch size cannot be strictly defined in this case. We also obtain the saturation density in such a patch as a function of the size of the patch and the relative carrying capacity of the outer region. We argue that this relative carrying capacity is a measure of the isolation of the patch. Our results are then compared with conclusions drawn from observations of the population dynamics of understorey birds in fragments of the Amazonian forest and shown to qualitatively agree with them, offering an explanation for the importance of dispersal and isolation in these observations. Finally, we show that a generalized critical patch size can be introduced resorting to threshold densities for the observation of a given species.

Antiparticle Contribution in the Cross Ladder Diagram for Bethe-Salpeter Equation in the Light-Front

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Description of Heavy Quark Mass by Lippmann-Schwinger Equation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the solutions of the position-dependent effective mass Schrodinger equation of a nonlinear oscillator related with the isotonic oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear Schrodinger equation for a superfluid Fermi gas in the BCS-BEC crossover

We introduce a quasianalytic nonlinear Schrodinger equation with beyond mean-field corrections to describe the dynamics of a zero-temperature dilute superfluid Fermi gas in the crossover from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where k(F)parallel to a parallel to << 1 with a the s-wave scattering length and k(F) the Fermi momentum, through the unitarity limit k(F)a ->+/-infinity to the Bose-Einstein condensation (BEC) regime where k(F)a > 0. The energy of our model is parametrized using the known asymptotic behavior in the BCS, BEC, and the unitarity limits and is in excellent agreement with accurate Green's-function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillations of a trapped Fermi superfluid.

Light composite Higgs boson from the normalized Bethe-Salpeter equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear two-field models from orbit equation deformations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)