Language of Instruction

English

Level of Course Unit

First Cycle

Department / Program

MATHEMATICS

Mode of Delivery

Face to Face

Type of Course Unit

Elective

Objectives of the Course

Study main properties on linear and nonlinear wave theory and show wide applications to hydrodynamic etc

Course Content

Linear Harmonic Oscillator: Simple, Damped, and Forced oscillations, Nonlinear oscillations, Fourier Transform and Convolution, Linear Wave Equations, Plane waves and Dispersion Relation, Linear Dispersive Waves, Wave packets, Nonlinear Waves, Inviscid Burgers equation, Formation of Shocks, Nonlinear diffusive waves and Viscous Burgers Equation, ColeHopf transform, Shock and Multishock traveling Wave solutions, SelfSimilarity solutions, Nonlinear Dispersive Waves, Kortewegde Vries equation (KdV) and Solitary waves, NonLinear Schrödinger equation and Solitons.

Course Methods and Techniques


Prerequisites and corequisities

None

Course Coordinator

None

Name of Lecturers

Prof.Dr. Şirin A. Büyükaşık

Assistants

None

Work Placement(s)

No

Recommended or Required Reading
Resources

Nonlinear Dynamics by M. Lakshmanan & S. Rajasekar, Springer, 2003. “Linear and Nonlinear Waves”, G. B. Whitham “Nonlinear waves, solitons and chaos”, E. Infeld, G. Rowlands









