Symmetry analysis is a powerful tool that enables the user to construct exact solutions of a given differential equation in a fairly systematic way. For this reason, the Lie point symmetry groups of most well-known differential equations have been catalogued. It is widely believed that the set of symmetries of an initial-value problem (or boundary-value problem) is a subset of the set of symmet...

We use Elie Cartan's method of equivalence to give a complete classification, in terms of differential invariants, of second-order ordinary differential equations admitting Lie groups of fibre-preserving point symmetries. We then apply our results to the determination of all second-order equations which are equivalent, under fibre-preserving transformations, to the free particle equation. In ad...

Tetra-n-butylammonium bromide forms the title semi-clathrate hydrate crystal, C16H36N+.Br-.38H2O, under atmospheric pressure. The cation and anion lie at sites with mm symmetry and seven water molecules lie at sites with m symmetry in space group Pmma. Br- anions construct a cage structure with the water molecules. Tetra-n-butylammonium cations are disordered and are located at the centre of fo...

Steady heat transfer through a pin fin is studied. Thermal conductivity, heat transfer coefficient, and the source or sink term are assumed to be temperature dependent. In the model considered, the source or sink term is given as an arbitrary function. We employ symmetry techniques to determine forms of the source or sink term for which the extra Lie point symmetries are admitted. Method of sep...

The generalized Drinfel’d-Sokolov hierarchies studied by de Groot-HollowoodMiramontes are extended from the viewpoint of Sato-Wilson dressing method. In the A (1) 1 case, we obtain the hierarchy that include the derivative nonlinear Schrödinger equation. We give two types of affine Weyl group symmetry of the hierarchy based on the Gauss decomposition of the A (1) 1 affine Lie group. The fourth ...

Abstract. We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a discrete-time setting as well as the standard continuous-time formulation. Specifically, we recast the optimal control problem as a constrained variation...

In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group ...

We carry out the extended symmetry analysis of an ultraparabolic Fokker-Planck equation with three independent variables, which is also called Kolmogorov and singled within class such equations by its remarkable properties. In particular, essential Lie invariance algebra eight-dimensional, maximum dimension above class. compute complete point pseudogroup using direct method, analyze structure s...

"Optimal systems" of similarity solutions of a given system of nonlinear partial (integro-)differential equations which admits a finite-dimensional Lie point symmetry group G are an effective systematic means to classify these group-invariant solutions since every other such solution can be derived from the members of the optimal systems. The classification problem for the similarity solutions ...