# Functional self-similarity and renormalization group symmetry in mathematical physics

@article{Kovalev1999FunctionalSA, title={Functional self-similarity and renormalization group symmetry in mathematical physics}, author={V. F. Kovalev and D. V. Shirkov}, journal={Theoretical and Mathematical Physics}, year={1999}, volume={121}, pages={1315-1332} }

The results from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the regular algorithm for finding renormalization group-type symmetries using the contemporary theory of Lie groups of transformations.

## 19 Citations

### Renorm-group symmetry for functionals of boundary value problem solutions

- Mathematics
- 2006

Recent advances in generalizing the renorm-group algorithm for boundary value problems of mathematical physics and the related concept of the renorm-group symmetry, previously formulated with…

### Analyzing jump phenomena and stability in nonlinear oscillators using renormalization group arguments

- Physics, Mathematics
- 2010

We study the stability of a damped Duffing oscillator by employing a renormalization group method for solving nonlinear differential equations. This approach is direct and makes the study of the…

### A Hint of renormalization

- Physics
- 2002

An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical…

### Renormalization group symmetry and initial value problem for shallow water equations

- Mathematics, Physics
- 2004

### Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups

- MathematicsJ. Appl. Math.
- 2015

An extended Lie group analysis method is provided that is also applicable to partial differential equations and makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior.

### New class of symmetries and exact solution to the unsteady equations of adiabatic gas dynamics

- Mathematics, Physics
- 2005

### One Property of the Renormalization Group Operator

- Physics
- 2004

We use an isotropic ferromagnet as an example to show that the renormalization group operator can be interpreted as an evolution operator for a system of spins evolving with an increase of the…

### Renormalization group and Lienard systems of differential equations

- Mathematics
- 2010

Autonomous Lienard systems, which constitute a huge family of periodic motions, exhibit limit cycle behaviour in certain cases and centres in others. In the literature, the signature for the…

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