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Showing 1 to 8 of 8 for “"Lie Symmetry"”.
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A New Approach to Lie Symmetry Groups of Minimal Surfaces
<p>The Lie symmetry groups of minimal surfaces by way of planar harmonic functions are determined. It is shown that a symmetry group acting on the minimal surfaces is isomorphic with H × H^2 — the analytic functions and the harmonic functions. A subgroup of this gives a generalization of the …
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A study of certain multi-dimensional partial differential equations using Lie symmetry analysis
… Boussinesq equations are obtained using the Lie symmetry method along with the simplest equation method. The solutions obtained are solitary waves and non-topological solution. Conservation laws for both equations are constructed using the new conservation theorem due to Ibragimov. Lie …
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Symbolic-numeric algorithms for simplifying differential systems and their application to the determination of approximate Lie symmetry algebras
… Differential elimination methods can be applied to these systems, which involve a finite number of differentiations and eliminations to reveal hidden constraints, and form the determining equations of symmetries. Normally, such PDE systems have approximate parameters, and the direct …
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Similarity Solutions for the Two-Dimensional Diffusion–Advection Equation in Sharp-Corner Geometries
… concentration profiles near sharp corners. The Lie symmetry method is applied to the 2D diffusion-advection equation to obtain a similarity ansatz, reducing the equation to a time-independent second-order PDE. By modifying the ansatz, the problem can be recast as an eigenvalue problem. …
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New methods for the integration of distributions of vector fields
… The generalization is rooted in the extension of Lie point symmetries to Cinf-symmetries for ODEs. We adapt this notion to the case of distributions of vector fields and use it to define Cinf-structures. The main result of the thesis is that the knowledge of a Cinf-structure for a given involutive …
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New symmetries from old: exploiting lie algebra structure to determine infinitesimal symmetries of differential equations
We give a method for using explicitly known Lie symmetries of a system of differential equations to help find more symmetries of the system. A Lie (or infinitesimal) symmetry of a system of differential equations is a transformation of its dependent and independent variables, depending on …
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Application of Lie symmetries to Solving Partial Differential Equations associated with the Mathematics of Finance
… we apply the algorithmic quantitative theory of Lie, the Lie symmetry analysis, to derive and solve the models associated with interest rate derivatives whose price dynamics comprise of partial differential equations in their set up. The interest rate derivative model that we consider is of great …
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Lie Analysis for Partial Differential Equations in Finance
… the price of an European option. We apply the Lie analysis theory to solve the PDEs, we provide the group classification and use it to find the invariant analytical solutions, particularly the ones compatible with the terminal conditions.