Twistor Theory and Differential Equations TeX Export

@article{citeulike:3998788, abstract = {This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon arise from holomorphic vector bundles over \$T\CP^1\$. A different framework is provided for the dispersionless analogues of soliton equations, like dispersionless KP or \$SU(\infty)\$ Toda system in 2+1 dimensions. Their solutions correspond to deformations of of (parts of) \$T\CP^1\$, and ultimately to Einstein--Weyl curved geometries generalising the flat Minkowski space. A number of exercises is included and the necessary facts about vector bundles over the Riemann sphere are summarised in the Appendix.}, archivePrefix = {arXiv}, author = {Dunajski, Maciej}, citeulike-article-id = {3998788}, citeulike-linkout-0 = {http://arxiv.org/abs/0902.0274}, citeulike-linkout-1 = {http://arxiv.org/pdf/0902.0274}, eprint = {0902.0274}, keywords = {calculation, differential\_equations, non\_linear\_differential\_equations, twistor\_theory}, month = {Feb}, posted-at = {2009-03-07 22:08:31}, priority = {2}, title = {Twistor Theory and Differential Equations}, url = {http://arxiv.org/abs/0902.0274}, year = {2009} }

TY - JOUR ID - citeulike:3998788 L3 - citeulike-article-id:3998788 N2 - This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon arise from holomorphic vector bundles over $T\CP^1$. A different framework is provided for the dispersionless analogues of soliton equations, like dispersionless KP or $SU(\infty)$ Toda system in 2+1 dimensions. Their solutions correspond to deformations of of (parts of) $T\CP^1$, and ultimately to Einstein--Weyl curved geometries generalising the flat Minkowski space. A number of exercises is included and the necessary facts about vector bundles over the Riemann sphere are summarised in the Appendix. TI - Twistor Theory and Differential Equations KW - calculation KW - differential_equations KW - non_linear_differential_equations KW - twistor_theory AU - Dunajski, Maciej PY - 2009/Feb/02/ UR - http://arxiv.org/abs/0902.0274 ER -