Stability and bifurcations of undulate solutions for one functional-differential equation

A periodic boundary-value problem for one nonlinear functional-differential equation is considered. This equation is well known as the nonlocal erosion equation. The case of small spatial deviation is studied. The possibility of the bifurcations for the spatial nonhomogeneous solutions is demonstrated. For these solutions, the asymptotical formulas are obtained and the stability is studied. All results are obtained with the help of the bifurcation theory.