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Center for Nonlinear Studies |
We investigated analytically and numerically the impact of nonlinear diffusion and dispersion on various nonlinear, conservative PDEs. These included the Korteweg-de Vries, Burgers, and regularized long-wave equations. Such evolution equations with nonlinear terms balance convective forces with diffusion or dispersion, and give rise to stable exotic waves with coherent structure. I will give a brief introduction on how to solve for special solutions of these equations and provide video clips (with popcorn!) to demonstrate the rich dynamic behavior. We will see traveling waves and diffusion fronts with compact support. We will also present stable solitary waves of nonintegrable equations that, much like solitons, collide nearly elastically.
Host: Markus Berndt