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Tytuł:
Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions
Autorzy:
Holzleitner, M.
Kostenko, A.
Teschl, G.
Powiązania:
https://bibliotekanauki.pl/articles/255331.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Schrödinger equation
dispersive estimates
scattering
Opis:
We investigate the dependence of the [formula] dispersive estimates for one-dimensional radial Schrödinger operators on boundary conditions at 0. In contrast to the case of additive perturbations, we show that the change of a boundary condition at zero results in the change of the dispersive decay estimates if the angular momentum is positive, l ∈ (0,1/2). However, for nonpositive angular momenta, l ∈ (—1/2,0], the standard [formula] decay remains true for all self-adjoint realizations.
Źródło:
Opuscula Mathematica; 2016, 36, 6; 769-786
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Initial value problem for the time-dependent linear Schrodinger equation with a point singular potential by the unified transform method
Autorzy:
Rybalko, Y.
Powiązania:
https://bibliotekanauki.pl/articles/255033.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Fokas unified transform method Schrodinger equation
interface problem
Opis:
We study an initial value problem for the one-dimensional non-stationary linear Schrodinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems on two half-lines, to which we apply the unified approach to IBV problems for linear and integrable nonlinear equations, also known as the Fokas unified transform method. Following the ideas of this method, we obtain the integral representation of the solution of the initial value problem.
Źródło:
Opuscula Mathematica; 2018, 38, 6; 883-898
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New optical solitary waves for unstable Schrödinger equation in nonlinear medium
Autorzy:
Zhou, Qin
Rezazadeh, Hadi
Korkmaz, Alper
Eslami, Mostafa
Mirzazadeh, Mohammad
Rezazadeh, Mohammadreza
Powiązania:
https://bibliotekanauki.pl/articles/173644.pdf
Data publikacji:
2019
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
solitons
new extended direct algebraic method
unstable Schrödinger equation
Opis:
In this paper and for the first time, we describe and introduce a new extended direct algebraic method which is a new method for solving nonlinear partial differential equations arising in nonlinear optics and nonlinear science. By applying this method, we have constructed new solitary wave solutions for the unstable Schrödinger equation. A large family of traveling wave type exact solutions covering exponential, generalized trigonometric, rational and generalized hyperbolic functions to this equation is determined. The solutions are expressed in explicit forms.
Źródło:
Optica Applicata; 2019, 49, 1; 135-150
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global well-posedness and scattering for the focusing nonlinear Schrödinger equation in the nonradial case
Autorzy:
Han, P.
Powiązania:
https://bibliotekanauki.pl/articles/254861.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
critical energy
focusing Schrodinger equation
global well-posedness
scattering
Opis:
The energy-critical, focusing nonlinear Schrödinger equation in the nonradial case reads as follows: [formula]. Under a suitable assumption on the maximal strong solution, using a compactness argument and a virial identity, we establish the global well-posedness and scattering in the nonradial case, which gives a positive answer to one open problem proposed by Kenig and Merle [Invent. Math. 166 (2006), 645-675].
Źródło:
Opuscula Mathematica; 2012, 32, 3; 487-504
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Quaternions and Cauchy Classical Theory of Elasticity
Autorzy:
Danielewski, Marek
Sapa, Lucjan
Powiązania:
https://bibliotekanauki.pl/articles/175624.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
wave mechanics
quaternions
Cauchy model
elastic solid
Schrödinger equation
Opis:
Developed by French mathematician Augustin-Louis Cauchy, the classical theory of elasticity is the starting point to show the value and the physical reality of quaternions. The classical balance equations for the isotropic, elastic crystal, demonstrate the usefulness of quaternions. The family of wave equations and the diffusion equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic solid. Using the quaternion algebra, we present the derivation of the quaternion form of the multiple wave equations. The fundamental consequences of all derived equations and relations for physics, chemistry, and future prospects are presented.
Źródło:
Advances in Manufacturing Science and Technology; 2020, 44, 2; 67-70
0137-4478
Pojawia się w:
Advances in Manufacturing Science and Technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the maximal operator associated with the free Schrödinger equation
Autorzy:
Wang, Sichun
Powiązania:
https://bibliotekanauki.pl/articles/1220332.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
free Schrödinger equation
maximal functions
spherical harmonics
oscillatory integrals
Opis:
For d > 1, let $(S_{d}f)(x,t) = ʃ_{ℝ^n} e^{ix·ξ} e^{it|ξ|^d} f̂(ξ)dξ$, $x ∈ ℝ^n$, where f̂ is the Fourier transform of $f ∈ S (ℝ^n)$, and $(S_{d}*f)(x) = sup_{0 < t < 1} |(S_{d}f)(x,t)|$ its maximal operator. P. Sjölin ([11]) has shown that for radial f, the estimate (*) $(\int_{|x| < R} |(S_{d}*f)(x)|^p dx)^{1//p} ≤ C_{R}∥f∥_{H_{1//4}}$ holds for p = 4n//(2n-1) and fails for p > 4n/(2n-1). In this paper we show that for non-radial f, (*) fails for p > 2. A similar result is proved for a more general maximal operator.
Źródło:
Studia Mathematica; 1997, 122, 2; 167-182
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical solutions of Schrödinger equation with new solvable potential family V(r)=A/r^2-B/r+Cr^(δ+1) via Nikiforov-Uvarov (NU) method
Autorzy:
Antia, Akaninyene Daniel
Akpan, Ita Okon
Ikot, Akpan Ndem
Maghsoodi, Elham
Zarrinkamar, Saber
Hassanabadi, Hassan
Powiązania:
https://bibliotekanauki.pl/articles/763317.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Schrödinger equation
Energy eigenvalue
Eigenfunction
Diatomic molecules
Hellmann-Feynmann theorem
Opis:
In this paper, we have presented the exact solutions of the Schrödinger equation with the family of potentials V(r)=A/r^2-B/r+Cr^(δ+1). We have obtained the energy eigenvalues and the corresponding wave functions expressed in terms of the associated Laguerre polynomials for  using the Nikiforov-Uvarov (NU) method. The energy levels for each case is computed for diatomic molecules H2, CO, NO and N2  for various values of and . We have also computed the expectation values of, and the Virial theorem using the Hellmann-Feynmann theorem (HFT).
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio AAA – Physica; 2015, 70
0137-6861
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio AAA – Physica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllable propagation of Pearcey–Gaussian beams in photorefractive media with fractional Schrödinger equation
Autorzy:
Guo, Teng
Gao, Ru
Ren, Shumin
Wang, Pengxiang
Xiao, Yan
Powiązania:
https://bibliotekanauki.pl/articles/2172852.pdf
Data publikacji:
2022
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
Pearcey-Gaussian beam
fractional Schrödinger equation
photorefractive medium
breathing soliton
Opis:
Taking the fractional Schrödinger equation as the theoretical model, the evolution behavior of the Pearcey–Gaussian beam in the photorefractive medium is studied. The results show that breathing solitons are generated when the nonlinear effect and the diffraction effect are balanced with each other. Nonlinear coefficients, Lévy index and beams amplitude affect breathing period of the soliton and maximum peak intensity. Within a certain range, the breathing period of the soliton decreases with the increase of the nonlinear coefficient and the Lévy index. However when the beams amplitude increases, the breathing period and the maximum peak intensity of the soliton increase. Under the photorefractive effect, due to the bidirectional self-acceleration property of the Pearcey beam, the solitons formed will propagate vertically. These properties can be used to manipulate the beam and have potential applications in optical switching, plasma channeling, particle manipulation, etc.
Źródło:
Optica Applicata; 2022, 52, 4; 627--638
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllabilty and stability analysis on a group associated with Black-Scholes equation
Autorzy:
Tiwari, Archana
Bhattacharyya, Debanjana
Pati, K. C.
Powiązania:
https://bibliotekanauki.pl/articles/229513.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Black-Scholes equation
Schrödinger equation
Lie group
optimal control
stability
numerical integration
Opis:
In this paper we have studied the driftless control system on a Lie group which arises due to the invariance of Black-Scholes equation by conformal transformations. These type of studies are possible as Black-Scholes equation can be mapped to one dimensional free Schrödinger equation. In particular we have studied the controllability, optimal control of the resulting dynamics as well as stability aspects of this system. We have also found out the trajectories of the states of the system through two unconventional integrators along with conventional Runge-Kutta integrator.
Źródło:
Archives of Control Sciences; 2020, 30, 3; 553-573
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Methods of mathematical quantum theory in selected economic models
Autorzy:
Schlichtinger, Agnieszka Matylda
Powiązania:
https://bibliotekanauki.pl/articles/584928.pdf
Data publikacji:
2018
Wydawca:
Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
Tematy:
Hilbert space
quaternions
quaternionic quantum mechanics
Schrödinger equation
regression
expected utility
Opis:
The issue of using the physical method in economics is no longer an innovative idea. However, nowadays the methods of mathematical quantum mechanics are also applied to economic sciences. This is the natural result of the fact that as applicable in quantum mechanics, mathematical spaces and tools turn out to be useful in other fields of science. Then it is possible to assume that the problem of the choice of the space is a universal question that is associated not only with mathematics and physics but also with economics or social sciences. In this paper the author considers various formulations of Hilbert space in relation to finite-dimensional quantum mechanics which constitutes a fundament to also apply my outcomes in economics. On the basis of mathematical considerations the author puts forward the hypothesis that the complex Hilbert space is characterized with numerous advantages in relation to its real and quaternionic alternatives.
Źródło:
Mathematical Economics; 2018, 14(21); 95-106
1733-9707
Pojawia się w:
Mathematical Economics
Dostawca treści:
Biblioteka Nauki
Artykuł
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