Geometries and Symmetries of Soliton equations and Integrable Elliptic equations

Details Geometries and Symmetries of Soliton equations and Integrable Elliptic equations Geometries and Symmetries of Soliton equations and Integrable Elliptic equations

2002-12-30

arxiv.org/abs/math/0212372v1

Mathematics

Differential Geometry

67 pages, to appear in Surveys on Geometry and Integrable Systems, Advanced Studies in Pure Mathematics, Mathematical Society

Scientific paper

We give a review of the systematic construction of hierarchies of soliton flows and integrable elliptic equations associated to a complex semi-simple Lie algebra and finite order automorphisms. For example, the non-linear Schr\"odinger equation, the n-wave equation, and the sigma-model are soliton flows; and the equation for harmonic maps from the plane to a compact Lie group, for primitive maps from the plane to a $k$-symmetric space, and constant mean curvature surfaces and isothermic surfaces in space forms are integrable elliptic systems. We also give a survey of (i) construction of solutions using loop group factorizations, (ii) PDEs in differential geometry that are soliton equations or elliptic integrable systems, (iii) similarities and differences of soliton equations and integrable elliptic systems.

Affiliated with

Also associated with

No associations

Rating

Geometries and Symmetries of Soliton equations and Integrable Elliptic equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometries and Symmetries of Soliton equations and Integrable Elliptic equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometries and Symmetries of Soliton equations and Integrable Elliptic equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-581172