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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 MAP 7119 .01 Advanced Nonlinear Dynamics Spring 2001 , 3 credit hours INSTRUCTOR Dr. Bhimsen K. Shivamoggi OFFICE MAP 104 OFFICE HOURS TR 9:00AM - 10:00AM PHONE 407-823-2061 EMAIL bhimsens@pegasus.cc.ucf.edu CLASS LOCATION    MAP 233 CLASS TIMES 5:30PM - 6:45PM TEXTBOOK See Listings Below by Various Authors GRADING POLICY Homework Assignments (totaling 80 points) and Individual Research Project (20 points). GRADING SCALE Average Grade 90 - 100% A 80 - 89% B 70 - 79% C 60 - 69% D 0 - 59% F IMPORTANT DATES Spring 2001 Classes Begin Jan.8; Late Registration and Add/Drop Jan.9-12; Application for Grade Forgiveness Deadline Jan.12; Fees Due and Last Day for Full Refund Jan.12; Withdrawal Deadline Mar.2; Classes End; Last Day to Remove Incomplete Apr.23; Final Examination Period Apr.24-30; Grades Due in Registrar's Office May 3; Grades Available on POLARIS and TouchTone May 4, after 9 a.m.; Commencements May 4-5 TENTATIVE LIST OF TOPICS •1. Nonlinear Differential Equations (Deterministic Problems, Equilibrium Points and Stability, Phase-plane Analysis, Non-autonomous Systems). •2. Bifurcation Theory (Saddle-node Transcritical and Pitchfork and Hopf Bifurcations). •3. Linear Dispersive Waves (Basic Features of Waves, General Solution of Wave Equation, Vibrating String, Beat Effect, Fourier Synthesis, Non-uniform Oscillatory Wavetrains). •4. Integrable Systems (Tests for Integrability: Singularity Analysis and the Painlevé Property for the Integrability of Nonlinear Ordinary/Partial Differential Equations). •5. Solitons (Generic Equations Possessing Soliton Solutions, Soliton Interactions, Inverse-scattering Transform Method, Backlünd Transformations connecting the Soliton Solutions). •6. Individual research projects. ••~••THE COURSE MATERIAL WILL BE BASED PRIMARILY ON THE FOLLOWING TEXTS: • 1. M.J. Ablowitz and P.A. Clarkson: Solitons – Nonlinear Evolution Equations, Cambridge University Press, (1995). •2. M.J. Ablowitz and H. Segur: Solitons and the Inverse Scattering Transform, SIAM Publications, (1981). •3. M. Tabor: Chaos and Integrability in Nonlinear Dynamics, Wiley, (1989). •4. E.A. Jackson: Perspectives in Nonlinear Dynamics, Vols. I & II, Cambridge University Press, (1991). •5. B.K. Shivamoggi: Nonlinear Dynamics and Chaotic Phenomena, Kluwer, (1997). •6. C.Gu: Soliton Theory and Its Applications, Springer, (1995). OTHER INFORMATION This is a second course in our Nonlinear Dynamics course sequence but can be taken by and large independent of the first course MAP 6118 Introduction to Nonlinear Dynamics. This course is aimed at providing students in applied mathematics, physics, and engineering with a sound analysis of the most important representative types of nonlinear phenomena in dynamical systems. This subject has enormous extent and variety with an increasingly diverse range of applications in physics and engineering like fluid dynamics, nonlinear mechanics and nonlinear optics. This is a 3 credit hour course, and the prerequisites are undergraduate courses, ordinary/partial differential equations (MAP 2302, MAP 4363 or equivalent), complex variables (MAP 4307 or equivalent) and an introductory mechanics course (PHY 3048 or equivalent). Previous exposure to MAP 6118: Introduction to Nonlinear Dynamics is useful but not mandatory.