Nonlinear Dynamics

The course introduces students to the current state of nonlinear wave mechanics problems. The students learn to solve these problems applying methods of mathematical and numerical modeling, with the use of Wolfram Mathematics.

Highlights of the course:

formulation of nonlinear wave problems of mechanics
nonlinear waves in a liquid
nonlinear waves in classic elastic body
nonlinear waves in media with internal structure

Students who have completed the course should be aware of up-to-date state of mechanics of deformable media, theoretical and applied mechanics. They should know how to formulate the major mechanics problems. Students have to be able to apply this knowledge to solve nonlinear dynamic problems of mechanics and conduct experimental studies using software packages. Students have to use methods of mathematical modelling for the analysis and solution of problems of natural science.

The course includes the following topics.

Formulation of nonlinear wave mechanics problems.
- Nonlinear simulation in liquid and solid.
- Derivation of nonlinear model equations.
- A comprehensive analytical and numerical approach to the study of solutions of equations with the help of the program Wolfram Mathematics.

Nonlinear waves in a liquid.
- Long waves in shallow water.
- Localized wave solutions of the model equations.
- Increasing of localized wave.
- The interaction of localized waves.

Nonlinear waves in classic elastic body.
- Localized deformation wave in the elastic rod.
- Localized deformation waves in crystals.
- Surface acoustic wave.