Results 31 to 40 of about 11,944 (302)
On a two-dimensional solvable system of difference equations
Electronic Journal of Qualitative Theory of Differential Equations, 2018 Here we solve the following system of difference equations $$x_{n+1}=\frac{y_ny_{n-2}}{bx_{n-1}+ay_{n-2}},\quad y_{n+1}=\frac{x_nx_{n-2}}{dy_{n-1}+cx_{n-2}},\quad n\in\mathbb{N}_0,$$ where parameters $a, b, c, d$ and initial values $x_{-j},$ $y_{-j}$, $j=
Stevo Stevic
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On quantum phase crossovers in finite systems [PDF]
, 2006 In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe ansatz solution ...
Hibberd, Katrina E. +2 more
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SciPost Physics, 2016 The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line, related to ...
T. Scoquart, J. J. Seaward, S. G. Jackson, M. Olshanii
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Two-dimensional product-type system of difference equations solvable in closed form [PDF]
, 2016 A solvable two-dimensional product-type system of difference equations of interest is presented. Closed form formulas for its general solution are given.A solvable two-dimensional product-type system of difference equations of interest is presented ...
Stevič, Stevo +5 more
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General solution to subclasses of a two-dimensional class of systems of difference equations
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We show practical solvability of the following two-dimensional systems of difference equations $$x_{n+1}=\frac{u_{n-2}v_{n-3}+a}{u_{n-2}+v_{n-3}},\quad y_{n+1}=\frac{w_{n-2}s_{n-3}+a}{w_{n-2}+s_{n-3}},\quad n\in\mathbb{N}_0,$$ where $u_n$, $v_n,$ $w_n ...
Stevo Stevic
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Solvability of systems of linear operator equations [PDF]
Proceedings of the American Mathematical Society, 1994 Let G G be a semigroup of commuting linear operators on a linear space
Jia, Rong-Qing +2 more
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On the solvability of a class of reaction‐diffusion systems [PDF]
Mathematical Problems in Engineering, 2006 We deal with a class of parabolic reaction‐diffusion systems. We use an iterative process based on results obtained for a linearized problem, then we derive some a priori estimates to establish the existence, uniqueness, and continuous dependence of the weak solution for a class of quasilinear systems.
Abdelfatah Bouziani, Ilham Mounir
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On a solvable system of difference equations of sixth-order
, 2023 In this paper, we study the following two-dimesional system of difference equations (Formula presented.), (Formula presented.), n ? N0; where the parameters a,b,c,d and the initial values x-i,y-i, i ? {1,2,3,4,5,6}, are real numbers.
Yazlik, Yasin +2 more
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Solvable product-type system of difference equations with two dependent variables
Advances in Difference Equations, 2017 It has been recently noticed that there is a finite number of two-dimensional classes of product-type systems of difference equations solvable in closed form. We present a new class of this type. A detailed analysis of the form of its solutions is given.
Stevo Stević
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A solvable system of difference equations [PDF]
, 2020 Summary: In this paper, we show that the system of difference equations \[x_n={\frac{ay^p_{n-1}+b(x_{n-2}y_{n-1})^{p-1}}{cy_{n-1}+dx^{p-1}_{n-2}}},\ y_n={\frac{{\alpha}x^p_{n-1}+{\beta}(y_{n-2}x_{n-1})^{p-1}}{{\gamma}x_{n-1}+{\delta}y^{p-1}_{n-2}}}, \] \(n\in \mathbb{N}_0\) where the parameters \(a, b, c, d, \alpha, \beta, \gamma, \delta, p\) and the ...
Taskara, Necati. +3 more
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