RESUMO
We analyze the modulation stability of spatiotemporal solitary and traveling wave solutions to the multidimensional nonlinear Schrödinger equation and the Gross-Pitaevskii equation with variable coefficients that were obtained using Jacobi elliptic functions. For all the solutions we obtain either unconditional stability, or a conditional stability that can be furnished through the use of dispersion management.
RESUMO
We apply the variational approach to solitons in highly nonlocal nonlinear media in D = 1, 2, 3 dimensions. We compare results obtained by the variational approach with those obtained by the accessible soliton approximation, by considering the same system of equations in the same spatial region and under the same boundary conditions. To assess the accuracy of these approximations, we also compare them with the numerical solution of the equations. We discover that the accessible soliton approximation suffers from systematic errors, when compared to the variational approach and the numerical solution. The errors increase with the dimension of the system. The variational highly nonlocal approximation provides more accurate results in any dimension and as such is more appropriate solution than the accessible soliton approximation.
Assuntos
Algoritmos , Luz , Modelos Teóricos , Dinâmica não Linear , Análise Numérica Assistida por Computador , Refratometria/métodos , Simulação por ComputadorRESUMO
We determine analytical extended traveling-wave and spatiotemporal solitary solutions to the generalized (3+1)-dimensional Gross-Pitaevskii equation with time-dependent coefficients, for the sinusoidally time-varying diffraction and quadratic potential strength. A number of periodic and localized solutions are obtained whose intensity does not decrease in time in the absence of externally induced gain or loss. Stability analysis of our solitary solutions is carried out, to display their modulational stability.
