Algebraic Methods in Physics: Nonlinear Differential Equations - M7022M

Period 1: 2015

Lecturer an Examiner: Prof. Norbert Euler, Mathematics, LTU

Note: This course is unfortunately no longer available at LTU.

The course aims to provide a general introdution to symmetry analysis of differential equations and will concentrate on the practical matters of how to derive and use symmetries of differential equations in order to calculate exact solutions and first integrals or conservation laws of nonlinear ordinary differential equations (ODEs) and nonlinear partial differential equations (PDEs). We'll also discuss some of the more recent developments regading nonlocal transformations between differential equations (for ODEs and PDEs) and the related classifcation problems, as well as some aspects of recursion operators for Lie-Baecklund symmetries of ODEs and PDEs and integrable hierarchies of differential equations.

Since this course consists of only ten lectures and given the wide range of subjects which we aim to include, we will not be able to discuss the deeper mathematical significance of some of the statements for the symmetry calculations. References will however be provided for the interested reader.

The course can be devided into the following main sections:
Complete Lecture Notes will be provided free of charge.

Additional books on this subject:
Credit System:
Exercises will be provided during class. Your solutions will determine your grades for this course.

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