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Wyświetlanie 1-15 z 21
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:
Propagation of solitary wave in non-uniform fiber system with high-order nonlinear effects
Autorzy:
Xiao, Y.
Zhang, J.
Zhang, L.
Powiązania:
https://bibliotekanauki.pl/articles/173308.pdf
Data publikacji:
2018
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
solitary wave
coupled higher-order nonlinear Schrödinger equation
high-order nonlinear effect
Opis:
The ultra-short pulse propagation in a non-uniform fiber system is investigated based on the variable coefficient coupled higher-order nonlinear Schrödinger equation with the dispersion gain and nonlinear gain terms. By using the ansatz method and the split-step Fourier method, we get the exact solitary wave solution, with which the transmission process of the solitary wave is studied. Furthermore we obtain the stability of the solitary wave under finite initial perturbations. The interaction between two neighboring solitary waves is also studied.
Źródło:
Optica Applicata; 2018, 48, 2; 273-284
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Theoretical analysis on experiments in transformation of deep-water-waves
Autorzy:
Wilde, P.
Powiązania:
https://bibliotekanauki.pl/articles/241349.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
water wave
stability
transformation
wave groups
non-linear Schrödinger differential equation
Opis:
The aim of the paper is to discuss the usefulness of the non-linear Schrödinger differential equation in the study of transformations of progressive deep water waves. Its solution compared with a regular Stokes type wave is essentially restricted to the first order approximation of the second one. The difference is that the Schrödinger equation introduces the concepts of a carrier wave and complex amplitude. In this way the dispersion relation of the third order Stokes expansion is taken into account. The analysis starts with regular, non breaking Stokes waves with large amplitudes as measured in our laboratory. The third order approximation is considered and compared with the corresponding solution of the Schrödinger equation. Then small periodic modifications are introduced in the time series fed into the control system of the generator. The approximation by trigonometric series is applied and the simplified analysis of superposition of very small modifications is used (higher powers of modifications are neglected). The Schrödinger non-linear equation is used in this analysis. The comparison of experimental and calculated envelopes is good, but for the surface elevations in space it is not as good. The approximation by trigonometric series is also applied to study the case of larger modifications. Finally the solutions of the Schrödinger equation corresponding to perfect solitons, are compared with the experimental data for cases where the measured surface elevations look almost like periodic solitons. This gives a reasonable approximation of the real behaviour in a very short space interval. It is not easy to get a good numerical description for the wave problem discussed as the waves are physically unstable. The results of the presented research will be used to establish an effective numerical procedure, stress the approximations introduced by the application of the Schrödinger differential equation and show how the theoretical solutions should be compared with the measured data.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2005, 52, 3; 213-242
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
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:
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
Tytuł:
Existence and uniqueness of the solution to the optimal control problem with integral criterion over the entire domain for a nonlinear Schrödinger equation with a special gradient term
Autorzy:
Salmanov, Vuqar
Powiązania:
https://bibliotekanauki.pl/articles/2050054.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Schrödinger equation
optimal control problem
first variation of the functional
complex potential
Opis:
The paper concerns the optimal control problem with the full-range integral performance criterion for the nonlinear Schrödinger equation with the specific gradient summand and the complex potential when the performance criterion is the full-range integral. In this paper, the existence and uniqueness theorems regarding the solution of the optimal control problem under consideration are proven.
Źródło:
Control and Cybernetics; 2020, 49, 3; 277-290
0324-8569
Pojawia się w:
Control and Cybernetics
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:
An Axiomatic Approach to Quantum Mechanics
Autorzy:
Rajakaruna, M. A. I. S.
Wijewardena Gamalath, K. A. I. L.
Powiązania:
https://bibliotekanauki.pl/articles/1076342.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Du Bois Raymond Lemma
Fisher Information
Quantum Mechanics
Schrödinger’s Wave Equation
Variational Principle
Opis:
We have shown that the Schrödinger wave equation can be explained and derived from fundamental postulates that are based on the conservation of probability, significance of measurements at infinity and nature’s tendency of maintaining a system as unbiased as possible. As a reasonable measure for the local randomness, Fisher information is considered. The presented approach provides an axiomatic derivation for the Schrödinger wave equation, avoiding imperfect models borrowed from classical mechanics such as direct application of the energy conservation, statistical mechanics or vibrating string models.
Źródło:
World Scientific News; 2019, 116; 209-221
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modulational instability of obliquely interacting capillary-gravity waves over infinite depth
Autorzy:
Manna, S.
Dhar, A. K.
Powiązania:
https://bibliotekanauki.pl/articles/38629088.pdf
Data publikacji:
2021
Wydawca:
Instytut Podstawowych Problemów Techniki PAN
Tematy:
nonlinear Schrödinger equation
crossing sea states
capillary-gravity waves
modulational instability
Opis:
Two coupled time-dependent two dimensional nonlinear Schrödinger equations have been derived using multiscale expansion for two nonlinearly interacting capillary-gravity waves over an infinite depth of water. These equations are then utilised to discuss the modulational (Benjamin-Feir) instability of two Stokes wavetrains due to unidirectional and bidirectional perturbations. It is found from the graphs and the three-dimensional contour plots that the rate of growth of instability for two wave packets interacting obliquely is higher than the instance of modulation of one wave packet. We have likewise examined the influence of capillarity on modulational instability.
Źródło:
Archives of Mechanics; 2021, 73, 5-6; 583-598
0373-2029
Pojawia się w:
Archives of Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical simulation of coupled quantum dots
Autorzy:
Machowska-Podsiadło, E.
Mączka, M.
Powiązania:
https://bibliotekanauki.pl/articles/378437.pdf
Data publikacji:
2006
Wydawca:
Sieć Badawcza Łukasiewicz - Instytut Technologii Elektronowej
Tematy:
kropki kwantowe
równanie Poissona
równanie Schrodingera
LDA
symulacja numeryczna
quantum dots
Poisson equation
Schrödinger equation
numerical simulation
Opis:
In the work we present self-consistent solutions of Poisson and Schrödinger equations which describe electron states in coupled quantum dots. Results for two neighbouring quantum dots formed in an electrostatic way are discussed. Zero-dimensional electron gas is investigated in the structure proposed by Kastner [1] and presented in our earlier works [2-4]. In the work results of simulations performed in three- and two-dimensional space are shown. We included Hartree potential for modeling Coulomb interactions among electrons in the system. We also considered the exchange and correlation potentials which ensured that each discrete energy level was occupied by only one electron. The exchange and correlation potentials were taken into account with the help of the Local Density Approximation (LDA).
Źródło:
Electron Technology : Internet Journal; 2005-2006, 37/38, 13; 1-4
1897-2381
Pojawia się w:
Electron Technology : Internet Journal
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Strzałka czasu a niektóre interpretacje mechaniki kwantowej
Time Arrow and Some Interpretations Of Quantum Mechanics
Autorzy:
Łagosz, Marek
Powiązania:
https://bibliotekanauki.pl/articles/2013391.pdf
Data publikacji:
2006
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
strzałka czasu
EPR-eksperyment
równanie Schrödingera
(a)symetria czasowa
niezmienniczość względem odwrócenia czasu
pomiar kwantowy
parametry ukryte
time arrow
EPR-experiment
Schrödinger’s equation
time (a)symetry
time- reversal invariance
quantal measurements
“hidden variables”
Opis:
In the paper I discuss some premises of “quantum mechanics” with regard to the thesis that the time arrow does (not) exist. In this context I consider above all the famous Einstein-Podolsky-Rosen’s experiment (EPR-experiment). I also indicate Schrödinger’s interpretation of wave function “symmetrical” towards time (nomological isotropy) and the peculiar understanding of the pair particle-antiparticle, assuming that the direction of time can be reversed. Eventually, I discuss the issue of measurement in quantum mechanics with which the existence of time arrow (anisotropy) is often linked. If it comes to the interpretations of quantum mechanics, from the point of which I consider the issues in question, then in principle I limit myself to two: the so-called Copenhagen interpretation and David Bohm’s conception of “hidden parameters.” I arrive at a conclusion that the premises of quantum mechanics that are at issue here cannot be sufficient grounds for a conclusive recognition of the reversibility (non-existence) of time arrow.
Źródło:
Roczniki Filozoficzne; 2006, 54, 2; 391-411
0035-7685
Pojawia się w:
Roczniki Filozoficzne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Efficient computation of the MCTDHF approximation to the time-dependent Schrodinger equation
Autorzy:
Koch, O.
Powiązania:
https://bibliotekanauki.pl/articles/255895.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
multi-configuration time-dependent Hartree-Fock method
time-dependent multi-particle Schrodinger equation
Coulomb potential
finite elements
Opis:
We discuss analytical and numerical properties of the multi-configuration time-dependent Hartree-Fock method for the approximate solution of the time-dependent multi-particle (electronic) Schrödinger equation which are relevant for an efficient implementation of this model reduction technique. Particularly, we focus on a discretization and Iow rank approximation in the evaluation of the meanfield terms occurring in the MCTDHF equations of motion, which is crucial for the computational tractability of the problem. We give error bounds for this approximation and demonstrate the achieved gain in performance.
Źródło:
Opuscula Mathematica; 2006, 26, 3; 483-497
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
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
Wyświetlanie 1-15 z 21

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