course number 203-2-4931

- Instabilities in physical systems: Rayleigh-Benard convection, self focusing and optical solitons, chemical oscillations, vegetation patterns.
- Mathematical analysis of instabilities: transcritical, saddle node, pitchfork and Hopf bifurcations.
- Primary instabilities in spatially extended systems: applications to convection and chemical oscillations.
- Amplitude equations: Non-Linear Shrodinger (NLS) equation, Newell-Whitehead-Segel (NWS) equation, Complex Ginzburg-Landau (CGL) equation.
- Secondary instabilities: Eckhaus, zigzag and Benjamin-Feir instabilities. Phase and amplitude turbulence.
- Front propagation in bistable systems: gradient vs. non-gradient systems, the non-equilibrium Ising-Bloch (NIB) bifurcation, transverse front instabilities.
- Singular perturbation theory of stationary and traveling patterns in bistable and excitable media.
- Spiral waves: kinematic theory, spiral turbulence.

- S.H. Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry and Engineering, (Addison-Wesley, Reading Mass., 1994). Q 172.5.C45S767.
- P. Manneville, Dissipative Structures and Weak Turbulence, (perspectives in Physics, New York, 1990). QA 871 .M33.
- A.C. Newell and J.V. Moloney, Nonlinear Optics, (Addison-Wesley, New York, 1992). QC446.2.N48.
- M. Cross and P .C. Hohenberg, Pattern Formation outside of Equilibrium, Rev. Mod. Phys. 65 (1993) 2.
- E. Meron, Pattern Formation in Excitable Media, Phys. Rep. 218 (1992) 1.

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