Linear Superposition of Nonlinear Waves
Analytical and Stochastic Fluid Dynamics
October 13, 2005 10:00 AM to 10:45 AM
Speakers:
|
 |
Abstract: |
Nonlinear waves are described by nonlinear differential equations. Their solutions are determined by initial data, which are functions of the spatial variables. When the equation is linear, if the initial function equals the sum of two or several functions, the solution equals the sum of corresponding solutions. For nonlinear equations this linear superposition principle is not valid. Nevertheless, there are important and physically relevant systems and classes of initial data for which the solution equals the sum of corresponding solutions with a small error. The examples include: Fermi-Pasta-Ulam system, nonlinear wave equation, nonlinear Schrodinger equation, Navier-Stokes and Euler systems in a rotating frame, Boussinesq system with a strong rotation or stratification. The described approximate linear superposition of nonlinear waves is explained by a destructive wave interference between different wavepackets in the process of their time evolution, this interference drastically reduces nonlinear interactions between the wavepackets. |
|
|
