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Titlebook: Symmetries and Applications of Differential Equations; In Memory of Nail H. Albert C. J. Luo,Rafail K. Gazizov Book 2021 Higher Education P

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Complex Methods for Lie Symmetry Analysis,stion that was begged in saying “when they are applicable.” When . they be applicable and why, or how, does the complex method work? We indicate some lines to pursue to try to find the answers, or at least partial answers, to these questions.
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,Group Analysis of the Guéant and Pu Model of Option Pricing and Hedging,or invariant solutions and invariant submodels search. The model with the linear execution costs function is reduced to the heat equation. Known results on this equation are applied to the study of the linear function case.
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One-Dimensional Flows of a Polytropic Gas: Lie Group Classification, Conservation Laws, Invariant aaws with the help of Noether’s theorem. These conservation laws are also recalculated for the gas dynamics variables in the Eulerian and mass Lagrangian coordinates. Additionally, invariant and conservative difference schemes are provided.
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On Involutive Systems of Partial Differential Equations,em of partial differential equations cannot exceed the order of this system. This criterion can also be useful for constructing computer algorithms for reducing a system of differential equations to an involutive form.
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Approximate Symmetry in Nonlinear Physics Problems,. Since that moment, the concept of approximate symmetries has been widely used for solving different problems of mathematical physics based on equations with a small parameter. The concept of approximate groups turned out to be in great demand in constructing renormalization-group symmetries used i
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One-Dimensional Flows of a Polytropic Gas: Lie Group Classification, Conservation Laws, Invariant ammetric flows, and spherically symmetric flows. The one-dimensional flow of a polytropic gas is described by one second-order partial differential equation in the Lagrangian variables. The Lie group classification of this PDE is performed. Its variational structure allows to construct conservation l
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