F10PD Pure Mathematics D

Dr Anastasia Doikou

Course co-ordinator(s): Dr Anastasia Doikou (Edinburgh).

Aims:

Solitons are localized travelling wave packets that maintain their shapes as they travel, and emerge unaltered after interacting with each other. Due to this “particle like” nature solitons are of mathematical significance and have a plethora of realistic applications including optical fibres, water wave & tsunami formation, Bose Einstein condensates and chemical reactions among others.

In fact the soliton is part of Heriot Watt history being discovered by J. S. Russell who noticed a solitary “wave of transition” that travelled for great distance on the Union canal just 1 mile from campus. In this course we will develop the methods to study and understand solitons. To achieve this we w ill first introduce basic quantum mechanical notions and in particular Schrödinger’s equation and use this as a background to study non linear systems that display soliton behaviour.

 

Detailed Information

Pre-requisite course(s): F19MC Complex Analysis Please see prerequisites under UG students Useful Links on the right hand side.

Location: Edinburgh.

Semester: 2.

Further information: Syllabus, Number of lectures, Assessment, Learning Outcomes.

SCQF Level: 10.

Credits: 15.