Lie symmetry method is applied to find analytic solutions of initial-boundaryvalue problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a manner highlighting the systematic procedure of extending the symmetry method for a PDE to investigate BVPs of the PDE. A comparative analysis of numerical and...

Based on the generalized symmetry group method presented by Lou and Ma [Lou and Ma, Non-Lie symmetry groups of (2 + 1)-dimensional nonlinear systems obtained from a simple direct method, J. Phys. A: Math. Gen. 38 (2005) L129], firstly, both the Lie point groups and the full symmetry group of the nonisospectral BKP equation are obtained, at the same time, a relationship is constructed between th...

The Lie symmetry group for 1+1 dimensional relativistic heat-conducting fluid is calculated for two different theories, Eckart and Israel-Stewart and a comparison between the group-invariant solutions has been made. Both fluids were founded to be physical acceptable in the sense that during the evolution of the fluid there are three velocity solutions that are decreasing exponentially for parti...

We introduce an extension to local principal component analysis for learning symmetric manifolds. In particular, we use a spectral method approximate the Lie algebra corresponding symmetry group of underlying manifold. derive sample complexity our various manifolds before applying it data sets improved density estimation.

Higher order symmetry operators for the wave equation with scalar and vector potentials are investigated. All scalar potentials which admit second order symmetry operators are found explicitly. Symmetries of partial differential equations are used for separation of variables [1], description of conservation laws [2], construction of exact solutions [3], etc. Before can be applied, symmetries ha...

The current paper recovers cubic–quartic optical solitons in fiber Bragg gratings having polynomial law of nonlinear refractive index structures. Lie symmetry analysis is carried out, starting with the basic analysis. Then, it followed through improved Kudryashov and generalized Arnous schemes. parameter constraints are also identified for existence such solitons. Numerical surface plots suppor...

Title of Dissertation: Control and Stabilization of a Class of Nonlinear Systems with Symmetry Vikram Manikonda, Doctor of Philosophy, 1998 Dissertation directed by: Professor P.S. Krishnaprasad Department of Electrical Engineering The focus of this dissertation is to study issues related to controllability and stabilization of a class of underactuated mechanical systems with symmetry. In parti...

Symmetries play important roles in mathematics, physics and mechanics. Since Noether unveiled the profound relations between symmetries and conservation laws, many researches on them were done [1–15]. Recently, symmetry theories have been extended to discrete mechanics and equations [16–25]. As we know, even tiny changes in symmetry, named as perturbation to symmetry, are of great importance fo...