Gabriela Matei - Academia.edu (original) (raw)
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Papers by Gabriela Matei
Balkan Journal of Geometry and Its Applications
Our paper introduces and studies the idea of multitime evolution in the context of solitons. Sect... more Our paper introduces and studies the idea of multitime evolution in the context of solitons. Section 1 presents some historical data about solitons. Section 2 defines the multitime sine-Gordon PDE, using a fundamental tensor and a linear connection. Section 3 describes the multitime sine-Gordon scalar solitons as special solutions of the multitime sine-Gordon PDE. Section 4 proves the existence of the multitime sine-Gordon biscalar solitons. Section 5 analyzes the geometric characteristics (fundamental tensor, linear connection) of the sine-Gordon PDE, showing the existence of an infinity of Riemannian or semi-Riemannian structures such that the new PDE is a prolongation of the sine-Gordon PDE. The “two-time” sine-Gordon geometric dynamics, which is presented here for the first time, shows that the sine-Gordon soliton is generated.
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
We address the problem of extending the complete integrability theory to multitime stochastic dif... more We address the problem of extending the complete integrability theory to multitime stochastic differential systems, using path independent curvilinear integrals. The main results include the multitime stochastic processes with volumetric dependence, the derivative of a stochastic process with respect to a multitime Wiener process and their description via the multitime diffusion PDEs, Hermite polynomials and Tzitzeica hypersurfaces. Any differentiable multitime stochastic process admits an expansion in series of Hermite polynomials. Geometrically, the constant level sets of multitime stochastic processes with volumetric dependence are a union of Tzitzeica hypersurfaces. The main results can be used to improve the spirometry techniques.
Balkan Journal of Geometry and Its Applications
In this paper, we introduce and explore some properties of two types of multitime partial differe... more In this paper, we introduce and explore some properties of two types of multitime partial differential equations, one as geometrical pro-longation of the reaction-diffusion Kolmogorov-Petrovskii-Piskunov PDE and another as geometrical prolongation of the reaction-diffusion PDE of ultra-parabolic-hyperbolic type. The original ideas include: geometric ingredients to build first order and second order partial derivative oper-ators, two multitime reaction-diffusion PDEs, techniques to obtain mul-titime solitons defined by a multitime reaction-diffusion PDE in a given direction and multitime solitons defined by a reaction-diffusion PDE of ultra-parabolic-hyperbolic type.
Multitime evolution PDEs for Rayleigh waves are considered, using geometrical ingredients capable... more Multitime evolution PDEs for Rayleigh waves are considered, using geometrical ingredients capable to build an ultra-parabolic-hyperbolic differential operator. Their soliton solutions are found based on appropriate hypotheses and Bernoulli ODEs. These multitime solitons develop complex behavior of deformation phenomena. Section 1 presents the single-time Rayleigh wave equations. Section 2 analyzes the geometric characteristics (fundamental tensor, linear connection, vector fields, tensor
Balkan Journal of Geometry and Its Applications
Our paper introduces and studies the idea of multitime evolution in the context of solitons. Sect... more Our paper introduces and studies the idea of multitime evolution in the context of solitons. Section 1 presents some historical data about solitons. Section 2 defines the multitime sine-Gordon PDE, using a fundamental tensor and a linear connection. Section 3 describes the multitime sine-Gordon scalar solitons as special solutions of the multitime sine-Gordon PDE. Section 4 proves the existence of the multitime sine-Gordon biscalar solitons. Section 5 analyzes the geometric characteristics (fundamental tensor, linear connection) of the sine-Gordon PDE, showing the existence of an infinity of Riemannian or semi-Riemannian structures such that the new PDE is a prolongation of the sine-Gordon PDE. The “two-time” sine-Gordon geometric dynamics, which is presented here for the first time, shows that the sine-Gordon soliton is generated.
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
We address the problem of extending the complete integrability theory to multitime stochastic dif... more We address the problem of extending the complete integrability theory to multitime stochastic differential systems, using path independent curvilinear integrals. The main results include the multitime stochastic processes with volumetric dependence, the derivative of a stochastic process with respect to a multitime Wiener process and their description via the multitime diffusion PDEs, Hermite polynomials and Tzitzeica hypersurfaces. Any differentiable multitime stochastic process admits an expansion in series of Hermite polynomials. Geometrically, the constant level sets of multitime stochastic processes with volumetric dependence are a union of Tzitzeica hypersurfaces. The main results can be used to improve the spirometry techniques.
Balkan Journal of Geometry and Its Applications
In this paper, we introduce and explore some properties of two types of multitime partial differe... more In this paper, we introduce and explore some properties of two types of multitime partial differential equations, one as geometrical pro-longation of the reaction-diffusion Kolmogorov-Petrovskii-Piskunov PDE and another as geometrical prolongation of the reaction-diffusion PDE of ultra-parabolic-hyperbolic type. The original ideas include: geometric ingredients to build first order and second order partial derivative oper-ators, two multitime reaction-diffusion PDEs, techniques to obtain mul-titime solitons defined by a multitime reaction-diffusion PDE in a given direction and multitime solitons defined by a reaction-diffusion PDE of ultra-parabolic-hyperbolic type.
Multitime evolution PDEs for Rayleigh waves are considered, using geometrical ingredients capable... more Multitime evolution PDEs for Rayleigh waves are considered, using geometrical ingredients capable to build an ultra-parabolic-hyperbolic differential operator. Their soliton solutions are found based on appropriate hypotheses and Bernoulli ODEs. These multitime solitons develop complex behavior of deformation phenomena. Section 1 presents the single-time Rayleigh wave equations. Section 2 analyzes the geometric characteristics (fundamental tensor, linear connection, vector fields, tensor