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