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We study generalized group actions on differentiable manifolds in the Colombeau framework, extending previous work on flows of generalized vector fields and symmetry group analysis of generalized solutions. As an application, we analyze…
In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method…
The Lie-group approach to the perturbative renormalization group (RG) method is developed to obtain an asymptotic solutions of both autonomous and non-autonomous ordinary differential equations. Reduction of some partial differetial…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
The complete group classification problem for the class of (1+1)-dimensional $r$th order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary values of $r$ greater than or equal to two. We find the…
The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…
By using the Lie's invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schr\"{o}dinger equations with variable coefficients. Starting from the equivalence generators we construct…
The basic principles of generalization of the group theoretical approach to the relativistic wave equations on curved spaces are examined. The general method of the determination of wave equations from the known symmetry group of a…
In this paper, we propose the invariant subspace approach to find exact solutions of time-fractional partial differential equations (PDEs) with time delay. An algorithmic approach of finding invariant subspaces for the generalized…
Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…
Lie symmetry group method is applied to study the Telegraph equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
In this paper, a family of variable-coefficient fifth-order KdV equations has been considered. By using an infinitesimal method based on the determination of the equivalence group, differential invariants and invariant equations are…
Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of differential equations. Effective new techniques…
The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
A relativistic formulation of reaction theory for nuclei with a dynamics given by a unitary representations of the Poincar\'e group is developed. Relativistic dynamics is introduced by starting from a relativistic theory of free particles…