Riemann surfaces and their applications in integrable systems
- Introduction: Riemann surfaces
- Holomorphic function
- De finition of a Riemann surface
- Examples of Riemann surfaces and Basic theorem of algebra
- Complex forms on Rimann surfaces. Part 1
- Complex forms on Riemann surfaces. Part 2
- Residues of meromorphic 1-forms
- Sum of residues. Part 2
- Sum of residues. Part 2 (Aplications)
- Divisors on Riemann surfaces
- Jacobi variety of a compact Riemann surface
- Jacobi variety
- Kadomtsev-Petviashvilli equation
- Abel map
- Abel theorem
- Applications Riemann surfaces in integrable systems. Korteweg-de Vries equation
- Lax representation of Korteweg-de Vries equation
- Commuting ordinary difierential operators
- Baker-Akhiezer function
- Soliton solutions of the Koretweg-de Vries equation
- The final assignment
