Related papers: Lie Group analysis of Plasma equilibrium equations
Showing that the location of the zeros of the partition function can be used to study phase transitions, Yang and Lee initiated an ambitious and very fruitful approach. We give an overview of the results obtained using this approach. After…
The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and…
We discuss how point transformations can be used for the study of integrability, in particular, for deriving classes of integrable variable-coefficient differential equations. The procedure of finding the equivalence groupoid of a class of…
When we consider a differential equation $\Delta=0$ whose set of solutions is ${{\cal S}}_\Delta$, a Lie-point exact symmetry of this is a Lie-point invertible transformation $T$ such that $T({{\cal S}}_\Delta)={{\cal S}}_\Delta$, i.e. such…
We study admissible transformations and Lie symmetries for a class of variable-coefficient Burgers equations. We combine the advanced methods of splitting into normalized subclasses and of mappings between classes that are generated by…
We propose a method for integrating the right-invariant geodesic flows on Lie groups based on the use of a special canonical transformation in the cotangent bundle of the group. We also describe an original method of constructing exact…
Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities…
We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-B\"acklund…
In this paper we study a classification of linear systems on Lie groups with respect to the conjugacy of the corresponding flows. We also describe stability according to Lyapunov exponents.
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed three-dimensional plasma systems in a way consistent with chaos theory is…
Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which…
We consider difference equations of order four and determine the one parameter Lie group of transformations (Lie symmetries) that leave them invariant. We introduce a technique for finding their first integrals and discuss the association…
Lie symmetry group method is applied to study for the higher order Camassa-Holm equation. The symmetry group and its optimal system are given. Furthermore, preliminary classification of its group invariant solutions, symmetry reduction and…
The method of nonlinear realizations is a convenient tool for building dynamical realizations of a Lie group, which relies solely upon structure relations of the corresponding Lie algebra. The goal of this work is to discuss advantages and…
Straightforward method for the derivation of linearized version of stochastic stability analysis of the nonlinear differential equations is presented. Methods for the study of large time behavior of the moments are exposed. These general…
A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady…
We present a pedagogical account of the Lee-Yang theory of equilibrium phase transitions and review recent advances in applying this theory to nonequilibrium systems. Through both general considerations and explicit studies of specific…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and…