SI3150 Integrabla icke-linjära system och solitoner 7,5 hp

Integrable Non-Linear Systems and Solitons

In the last thirty years important progress was made in the understanding of certain non-linear differential equations which arise in several different areas of physics (e.g. plasma-, solid state-, bio-, elementary particle physics etc.). A common interesting feature is the occurrence of soliton solutions, i.e. stable, non-dissipative and localized configurations behaving in many ways like particles. These completely soluble non-linear equations now provide a substantial extension of the 'tool kit' of physicists. The subject is also fascinating due to its mathematical beauty and its surprising relations to other topics in mathematics and physics.

  • Utbildningsnivå

    Forskarnivå
  • Kursnivå (A-D)

    D
  • Huvudområde

  • Betygsskala

Det finns inget planerat kurstillfälle.

Lärandemål

This course gives a self-contained introduction to soliton equations. After the course one should have aquired an active knowledge of the course material (i.e. know about and be able to apply and generalize it) and be able to read research papers on the subject.

Kursens huvudsakliga innehåll

Soliton equations: what are they, where do they arise. What is special about these equations: Symmetries, conservations laws, Lax pairs. KdV equation: physical background, applications, how to solve it. Inverse scattering method. Other soliton equations. Hirota's method.

Behörighet

Grundläggande kurs i teorin för differentialekvationer.

Litteratur

  • Compendium by Edwin Langmann.
  • P. G. Drazin & R. S. Johnson: Solitons: An Introduction, Cambridge Texts in Applied Mathematics, 1989.

Examination

Krav för slutbetyg

Hemuppgifter och muntlig tentamen.

Ges av

SCI/Fysik

Kontaktperson

Edwin Langmann (langmann@kth.se)

Examinator

Edwin Langmann <langmann@kth.se>

Versionsinformation

Kursplan giltig från och med VT2009.