Integrable Surfaces: Riemannian Geometry and Group Theory

The following sections are included:

• Basic Ideas

• Pseudospherical Surfaces: SG, KdV, mKdV, ShG

• Spherical Surfaces: NLS, SG, NSM

  • Nonlinear Schrödinger equation

  • Sine–Gordon equation revisited

  • Nonlinear sigma model and SG equation

  • Spherical and pseudospherical surfaces

• Bäcklund Transformations Revisited

  • A Bäcklund transformation

  • Self-Bäcklund transformation

• Immersion of Integrable Surfaces on Lie Groups

  • A surface ∑² in ℝ³

  • Surfaces on Lie groups and Lie algebras

  • Nonlinear Schrödinger surfaces

• Mapping of Integrable Systems to Spherical Surfaces