Solitons in Modern Perspective

Lecturer: D. Fioravanti (INFN Researcher), Joint Course with SNS Pisa

Duration: 12 hours in April and May

Programme:

  • A bit of history: solitons in action from Scott Russel to Fermi and the modern times;
  • Dissipation and non-linearity in field equations;
  • Solitary waves and solitons;
  • The one kink, solitary wave and soliton solution for several equations;
  • Lagrangean and Hamiltonian formulation;
  • The problem of multi-soliton solutions; where is Liouville integrability? 
  • Hints on Baecklund transformations and differential geometry (of Sine-Gordon eq.);  
  • An educated use of Schroedinger eq.: the inverse scattering solution of the multi-soliton solution;
  • The Gelfand-Levitan and Marchenko equation;
  • Its general solution and the tau-function;
  • (What does the tau-function teach us about higher dimensional instantons?)
  • (About string solitons and instantons?)