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...

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 ...

"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 ...

Lie Group Action. A process by which a Lie group, acting as a symmetry, moves points in a space. When points in the space that are related by a group element are identified, one obtains the quotient space. Free Action. An action that moves every point under any nontrivial group element. Proper Action. An action that obeys a compactness condition. Momentum Mapping. A dynamically conserved quanti...

The applications of symmetry groups to problems arising in the calculus of variations have their origins in the late papers of Lie, e.g., [34], which introduced the subject of “integral invariants”. Lie showed how the symmetry group of a variational problem can be readily computed based on an adaptation of the infinitesimal method used to compute symmetry groups of differential equations. Moreo...

We establish an algebraic structure for zero curvature representations of coupled integrable couplings. The adopted zero curvature representations are associated with Lie algebras possessing two sub-Lie algebras in form of semi-direct sums of Lie algebras. By applying the presented algebraic structures to the AKNS systems, we give an approach for generating τ -symmetry algebras of coupled integ...

Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial first-order approximate symmetry.

We show that any Lie point symmetry of semilinear Kohn-Laplace equations on the Heisenberg group H with power nonlinearity is a divergence symmetry if and only if the corresponding exponent assumes critical value.

Lie symmetry group method is applied to study the Fisher-Kolmogorov equation. The symmetry group is given, and travelling wave solutions are obtained. Finally the conservation laws are determined.