The multidimensional nonlinear Schrödinger equation governs the spatial and temporal evolution of an optical field inside a nonlinear dispersive medium. Although spatial (diffractive) and temporal (dispersive) effects can be studied independently in a linear medium, they become mutually coupled in a nonlinear medium. We present the results of numerical simulations showing this spatiotemporal co...

It is well known that when a narrow-band signal propagates in any medium with sufficient length of the path, amplitude-frequency spectrum inevitably begins to deform due dispersion absorption coefficient medium, is, dependence on frequency. Therefore, time «at infinity» significantly depends not only real part refractive index, but also absorption. In this work, we consider propagation and dist...

5 [1] We study the influence of buoyancy and spatial heterogeneity on the spreading of the 6 saturation front of a displacing fluid during injection into a porous medium saturated 7 with another, immiscible fluid. To do so we use a stochastic modeling framework. We 8 derive an effective large‐scale flow equation for the saturation of the displacing fluid that 9 is characterized by six nonlocal ...