Physics

Formative targets: The objectives of the course are to bring the student to a deep knowledge and understanding of the basic mathematical properties i) of the nonlinear wave propagation with or without dispersion or dissipation; ii) of the construction of nonlinear mathematical models of physical interest, through the multiscale method, like the soliton equations, and of the mathematical techniques to solve them, arriving to the introduction of current research topics in the theory of solitons and anomalous waves. At the end of the course the student must be able i) to apply the acquired methods to problems in nonlinear physics even different from those studied in the course, in fluid dynamics, nonlinear optics, theory of gravitation, etc .., solving typical problems of the nonlinear dynamics; ii) to integrate in autonomy the acquired knowledges through the suggested literature, to solve also problems of interest for him/her, and not investigated in the course. The student will have the ability to consult supplementary material, interesting scientific papers, having acquired the right knowledges and critical skill to evaluate their content and their potential benefits to his/her scientific interests. At last the student must be able to conceive and develop a research project in autonomy. In order to achieve these goals, we plan to involve the student, during the theoretical lectures and exercises, through general and specific questions related to the subject; or through the presentation in depth of some specific subject agreed with the teacher.