Rapidly oscillating spatially inhomogeneous structures in coherent nonlinear optical systems

摘要

In [1], a number of mixing diffraction nonlinear effects in optics were modeled by using the parabolictype equation ?u/?t+u=??~2u/?x~2+Ksinu(t,x-h) (1) with deviating spatial variable and the periodic boundary conditions u(t,x+2π)≡ u(t, x).(2) Here, ε < 0 is the diffraction coefficient h < 0 is the argument shift (in normalized variables). In [1], the corresponding structural schemes of distributed feed-back systems were given; it was shown on the basis of numerical investigations that, in the boundary value problem (1), (2), moving periodic structures may arise. In [2], an effort to explain some results of [1] on the basis of a special local analysis method developed in [3] was made. In this paper, we show that the boundary value problem (1), (2) may possess a rich set of structures rapidly oscillating with respect to the spatial variable.