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Computing Cauchy integrals
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Classroom Contents
The Computational Theory of Riemann-Hilbert Problems - Lecture 4
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- 1 Integrable systems in Mathematics, Condensed Matter and Statistical Physics
- 2 The computational theory of Riemann-Hilbert problems Lecture 4
- 3 Computing Cauchy integrals
- 4 A controlled basis
- 5 Generalizing the contours
- 6 A definition and a singular integral equation
- 7 Sobolev spaces
- 8 Zero-sum space
- 9 Regularity of the jump matrix
- 10 Associated operators
- 11 Smoothness
- 12 Some notes on numerical solutions
- 13 The numerical solution of Riemann- Hilbert problems
- 14 The defocusing nonlinear Schrodinger equation
- 15 The initial value problem
- 16 An important calculation
- 17 Steepest descent
- 18 [Code Walkthrough]
- 19 A deformation
- 20 The KdV equation
- 21 The KdV equation with decaying data
- 22 Nonlinear superposition
- 23 With some solitons
- 24 Other work
- 25 Deformations
