Course Contents

Nonlinearity and Non Linear Effects, Method of multiple scales, Superposition principle, Harmonic and anharmonic oscillators, Pendulum, rotations and oscillation, Resonance producing secular terms, Phase portrait, Elliptic and Hyperbolic points, KDV equation solitary limit, Relation between amplitude, Nonlinear Schrodinger equation, Sagdeev potential, Driven damped Duffing oscillator, Non Linear Resonance, Deterministic Chaos, Logistic Map Population Biology, Fixed Points and Stability of 1-D maps , Time Series, Transients and Attractors , Graphical representation , Period Doubling Butterfly Effect , Periodic and Chaotic attractors, Bifurcation Diagram , Lyapunov Exponent for I-D map, Maps and Flows, Phase Space Dimensionality, Dynamical system, Fixed points and stability ,Characteristic Equation, stability Criteria ,Dissipative and Conservative systems ,Attractors and phase space volume contraction, Non intersection of trajectories, Wave equation and Dispersion Relation, Dispersive Waves, Phase velocity and group velocity, Types of Linear waves, Superposition principle, Carrier wave and wave modulation, Amplitude dependent phase velocity and Non Linear effects, Reductive Perturbation Method