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MATH3231: SOLITONS III

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Type Open
Level 3
Credits 20
Availability Available in 2024/2025
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • Complex Analysis II (MATH2011) AND Analysis in ManyVariables II (MATH2031).

Corequisites

  • None.

Excluded Combinations of Modules

Aims

  • To provide an introduction to solvable problems in nonlinear partial differential equations which have a physical application.
  • This is an area of comparatively recent development which stillpossesses potential for growth.

Content

  • Nonlinear wave equations.
  • Progressive wave solutions.
  • Backlund transformations for Sine Gordonequation.
  • Backlund transformations for KdV equation.
  • Conservation laws in integrable systems.
  • Hirota's method.
  • The Nonlinear Schrodinger equation.
  • The inverse scattering method.
  • The inverse scattering method: two componentequations.
  • Toda equations.
  • Integrability.

Learning Outcomes

Subject-specific Knowledge:

  • By the end of the module students will:
  • be able to solve novel and/or complex problems inSolitons.
  • have a systematic and coherent understanding of theoreticalmathematics in the field of Solitons.
  • have acquired coherent body of knowledge of these subjectsdemonstrated through one or more of the following topic areas:
  • Nonlinear wave equations.
  • Progressive wave solutions.
  • Backlund transformations for the sine-Gordon equation and theKdV equation.
  • Conservation laws in integrable systems.
  • Hirota's method.
  • The nonlinear Schrodinger equation.

Subject-specific Skills:

  • In addition students will have specialised mathematicalskills in the following areas which can be used with minimal guidance:Modelling, spatial awareness.

Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • Lectures demonstrate what is required to be learned and theapplication of the theory to practical examples.
  • Assignments for self-study develop problem-solving skills andenable students to test and develop their knowledge andunderstanding.
  • Formatively assessed assignments provide practice in theapplication of logic and high level of rigour as well as feedback forthe students and the lecturer on students' progress.
  • The end-of-year examination assesses the knowledge acquiredand the ability to solve predictable and unpredictableproblems.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week for 20 weeks and 2 in term 31 Hour42 
Problems Classes8Four in each of terms 1 and 21 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 Hours100 

Formative Assessment

Eight assignments to be submitted.

More information

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