PI: Weinstein DMS-9500997 Weinstein will study the role of nonlinear ground states in the dynamics of nonlinear dispersive evolution equations. Specific problems to be considered include the infinite time behavior of nonlinear dispersive Hamiltonian systems, the spectral stability and instability of nonlinear bound states, nonlinear waves in optical fibers and the dynamics of coupled fiber arrays, and vector Zakharov and vector nonlinear Schroding equations. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.
