The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, related field theories. Previous work has shown that this an explicit realisation self-dual YM where the equation of motion can be written a form maps directly to Pleba\'nski's heavenly for gravity. involves area-preserving diffeomorphism algebra, two copies which appear equation. In paper, we s...

Zheng Wang 1,*, Bochen Liu 1, Yue Zhang 1, Ming Cheng 1, Kai Chu 1 and Liang Xu 2 1 School of Electrical Engineering, Southeast University, Nanjing 210096, China; [email protected] (B.L.); [email protected] (Y.Z.); [email protected] (M.C.); [email protected] (K.C.) 2 Aviation Key Laboratory of Science and Technology on Aerospace Electromechanical System Integration, No. 33 Shuige Road, Jiang...

I Acknowledgements This thesis emerged from my time as a research assistant at the Intelligent Sensor Actuator (ISAS) lab at the Karlsruhe Institute of Technology (KIT). During my work on this thesis, I was supported by many people in various ways. At this point, I would like to appreciate especially those mentioned below. First and foremost, my deepest gratitude goes to Uwe D. Hanebeck for adv...

Using the heavenly equation as an example, we propose the method of group foliation as a tool for obtaining non-invariant solutions of PDEs with infinite-dimensional symmetry groups. The method involves the study of compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup and therefore selects exactly one orbit of solutions. By...

We provide an exact regular solution of an operator system arising as the prolongation structure associated with the heavenly equation. This solution is expressed in terms of operator Bessel coefficients. 1991 MSC: 83C20,35A30,58G35,33C10.

Christian Basarke, Institut für Software Systems Engineering, Technische Universität Braunschweig, [email protected] Christian Berger, Institut für Software Systems Engineering, Technische Universität Braunschweig, [email protected] Kai Homeier, Institut für Betriebssysteme und Rechnerverbund, Technische Universität Braunschweig, [email protected] Prof. Dr. Bernhard Rumpe, Institut für...

We have recently solved the inverse scattering problem for one parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations connected with the commutation of multidimensional vector fields, like the heavenly equation of Plebanski, the dispersionless Kadomtsev Petviashvili (dKP)...