American Institute of Mathematics, Palo Alto, California
Christopher K.R.T. Jones, Yuri Latushkin, Robert Pego, Arnd Scheel, and Bjorn Sandstede
Substantial progress in the understanding of the spectral stability of nonlinear waves in one-dimensional media has recently been achieved by systematically extending and refining the Evans function, an analytic function whose roots are in one-to-one correspondence with isolated eigenvalues of the linearization about a wave. Using robustness properties of topological indices and the computational advantages associated with the fact that a single analytic function captures all eigenvalues, stability and instability criteria for shock waves in viscous conservation laws, for solitons in coupled nonlinear Schrodinger equations, and for fronts and pulses in singularly perturbed reaction-diffusion systems have been derived.
The main emphasis of this workshop is to extend the construction of the Evans function to several space dimensions and to develop easily computable stability criteria for nonlinear waves such as vortices in the family of nonlinear Schrodinger equations, spiral waves in reaction-diffusion systems, and lump solutions in dispersive systems.
The workshop schedule.
A report on the workshop activities.
Yuri Latushkin's talk.