Spots and stripes in nonlinear Schrodinger-type equations with nearly one-dimensional potentials

We consider the existence of spots and stripes for a class of nonlinear Schrodinger-type equations in the presence of nearly one-dimensional localized potentials. Under suitable assumptions on the potential, we construct various types of waves that are localized in the direction of the potential and have single- or multihump, or periodic profile in the perpendicular direction. The analysis relies upon a spatial dynamics formulation of the existence problem, together with a center manifold reduction. This reduction procedure allows these waves to be realized as unipulse or multipulse homoclinic orbits, or periodic orbits in a reduced system of ordinary differential equations. Copyright (c) 2013 John Wiley & Sons, Ltd.