Corso di laurea in Fisica

The physics of nonlinear waves

Anno accademico 2009/2010

Sommario insegnamento

• Programma
• Strumenti didattici

Programma

Topics of the Course
The focus of this course is to address the influence of nonlinearity on the physics
of waves in a wide range of areas of classical and quantum physics: Applications
considered include the study of:
(1) Hydrodynamics and Turbulence
(2) Ocean surface and internal waves
(3) Nonlinear optics
(4) Fiber optics communications
(5) Solid state physics
(6) Quantum Field Theory
(7) Acoustic wave propagation in the Ocean

Outline of the Course
(1) The Fermi-Pasta-Ulam problem
(2) The discovery of the soliton by Zabusky and Kruskal
(3) The discovery of the Inverse Scattering Transform on the infinite line
(4) The discovery of IST for periodic boundary conditions
(5) Multidimensional problems for which IST gives approximate solutions
(6) Overview of periodic solutions and methods, including Riemann theta functions
(7) Riemannian methods for solving the Jacobian inverse problem and for solving
nonlinear partial differential equations: Generalized Fourier Analysis
(8) Application to the analysis of experimental nonlinear wave data
(9) Oceanic internal solitons
(10)-Oceanic freak, rogue or giant waves
(11)-Acoustic wave solitons and their influence on acoustic wave propagation

Highlights of the Course
(1) The original film of Zabusky and Kruskal (1962) (Bell Systems Laboratories and
Princeton) in which documents the discovery of solitons and soliton dynamics.
(2) A film from the BBC program “Horizon” called Freak Wave in which the general
topic of giant oceanic surface waves is covered. Work done here in Torino is
given extensive coverage in the film.
(3) Films (made by the Torino Nonlinear Wave Group) of numerical simulations of
giant waves made with the application of Riemann theta functions.

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