2013/12/18 by Shabnam Beheshti, Beheshti, Shabnam, A. Shadi Tahvildar‐Zadeh +1
Mathematics · Physics and Astronomy · Engineering · #Numerical methods for differential equations #Nonlinear Waves and Solitons #Dynamics and Control of Mechanical Systems
paper · pdf · doi:10.48550/arxiv.1312.5253
Motivated by integrability of the sine-Gordon equation, we investigate a\ntechnique for constructing desired solutions to Einstein's equations by\ncombining a dressing technique with a control-theory approach. After reviewing\nclassical integrability, we recall two well-known Killing field reductions of\nEinstein's equations, unify them using a harmonic map formulation, and state\ntwo results on the integrability of the equations and solvability of the\ndressing system. The resulting algorithm is then combined with an asymptotic\nanalysis to produce constraints on the degrees of freedom arising in the\nsolution-generation mechanism. The approach is carried out explicitly for the\nEinstein vacuum equations. Applications of the technique to other geometric\nfield theories are also discussed.\n