Whitham linear and nonlinear waves pdf
Gerald B. Whitham - WikipediaSolitary waves are special solutions to nonlinear PDEs which arise due to a perfect balance between linear dispersive and nonlinear effects. They are localized disturbances that, as the name suggests, evolve without any change to their shape. In cases of completely integrable PDEs they are called solitons. Solitary waves appear in real world as, for instance, laser generated pulses, tidal bores, morning glory clouds, freak waves, tsunami, wakes of high speed ships, etc. In this seminar, after briefly covering the history of solitary wave research, we will define a plane wave, phase velocity, wavepacket, group velocity, dispersion relation and the slowly varying envelope approximation.
Linear and Nonlinear Waves
Home Dates and deadlines Travel information Programme Contact. A family of solitary-wave solutions is found using a constrained minimisation principle and concentration-compactness methods for noncoercive functionals. The solitary waves are approximated by scalings of the corresponding solutions to partial differential equations arising as weakly nonlinear approximations; in the case of the Whitham equation the approximation is the Korteweg-deVries equation. We also demonstrate that the family of solitary-wave solutions is conditionally energetically stable. Using harmonic maps we provide an approach towards obtaining explicit solutions to the incompressible two-dimensional Euler equations. While the general solution is not available in explicit form, the structural properties of the system permit us to identify several classes of explicit solutions.
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