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Numerical methods in theory of topological solitons

Study and application of various numerical techniques in construction of solitons in scalar field theories in flat and curved spacetime

Tasks

1. Numerical counstruction of kink and oscillon solutions in 1+1 dim phi4 theory
2. Soliton solutions of the planar O(3) sigma model
3. Skyrmions in 2d and 3d
4. Black holes with Skyrmion hairs

Preliminary schedule by topics/tasks

- Numerical counstruction and investigation of the collision dynamics of the kinks and oscillons in phi4 theory
- Application of the rational map construction in the non-linear O(3) sigma model
- Topological solitons of the Skyrme model
- Hairy black holes

Required skills

- basic knowledge of classical field theory and general relativity
- minimal experience with scientific programming (c++)

Acquired skills and experience

- understanding of the role of topological solitons in field theory
- practical application of various numerical methods in modern classical field theory

Recommended literature

1. Ya Shnir, Topological and Non-Topological Solitons in Scalar Field Theories, Cambridge University Press, 2018
2. N Manton and P Sutcliffe, Topological Solitons, Cambridge University Press, 2005
3. W Press et al, Numerical Recipes 3rd Edition: The Art of Scientific Computing, Cambridge University Press 2007