scholarly journals Riccati Generalized Resonant States of Higher-order Nonlinear Schrӧdinger Equation With Pӧschl-teller Potential

2021 ◽  
Author(s):  
Nisha Kadian ◽  
Sanjana Bhatia ◽  
Shailza Pathania ◽  
Amit Goyal ◽  
Nagaraja Kumar Choragudi
Keyword(s):  
Hypergeometric Functions ◽  
Resonant State ◽  
Higher Order ◽  
Hamiltonian Approach ◽  
Localized Solutions ◽  
Resonant States

Abstract We present resonant state solutions of the higher-order nonlinear Schrӧdinger model, with Pӧschl-Teller (PT) potential, under certain parametric conditions. It is found that the localized solutions can be expressed in terms of the hypergeometric functions F(a, b, c; z). The dynamics of these resonant states and their control using isospectral Hamiltonian approach is well illustrated for PT potential, which is analytically tractable.

Three-alpha resonant state and its contribution in continuum spectrum

2006 ◽  
Vol 21 (31n33) ◽  
pp. 2351-2358
Author(s):  
C. Kurokawa ◽  
K. Katō
Keyword(s):  
Boundary Condition ◽  
Resonant State ◽  
Level Density ◽  
Complex Scaling ◽  
Scaling Method ◽  
Complex Scaling Method ◽  
Resonant States ◽  
Complex Eigenvalues ◽  
Three Body ◽  
The Continuum

The 3α resonant states of 12 C are investigated by taking into account the correct boundary condition for three-body resonant states. In order to show how the 3α resonant states having complex eigenvalues contribute to the real energy, we calculated the Continuum Level Density in the Complex Scaling Method.

scholarly journals The Influence of Mesh Granularity on the Accuracy of FEM Modelling of the Resonant State in a Microwave Chamber

2021 ◽  
Vol 11 (17) ◽  
pp. 7932
Author(s):  
Anna Ostaszewska-Liżewska ◽  
Dominika Kopala ◽  
Jakub Szałatkiewicz ◽  
Roman Szewczyk ◽  
Peter Råback
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Open Source ◽  
Resonant State ◽  
Point Of View ◽  
Tetrahedral Mesh ◽  
Efficient Design ◽  
Resonant States ◽  
Main Barrier ◽  
Element Method

Microwave technology is widely used in different areas of advanced industry when energy must be provided to water-containing and other materials. The main barrier in the development of microwave devices is the possibility of efficient design by modelling a microwave system in a resonant state. For technical systems, the finite element method is widely used. However, the convergence process in the microwave finite element solver is sophisticated. The process itself and the influence of mesh granularity on the accuracy of modelling of microwave chambers in resonant states have not been investigated previously. The present paper aims to fill this gap. The resonance conditions of a microwave chamber were tested from the point of view of spatial resolution of the tetrahedral mesh used for open-source ELMER FEM software. The presented results experimentally determine the limits of accuracy of the geometry of microwave resonant chamber finite element method-based models. The determined values of microwave resonant chamber dimension tolerances should be considered for both open-source and commercial software for microwave modelling.

Exotic Resonant States for One-Dimensional Twin Complex Square Potentials

2013 ◽  
Vol 68 (10-11) ◽  
pp. 587-598
Author(s):  
Cornelia Grama ◽  
Nicolae Grama ◽  
Ioan Zamfirescu ◽  
Horia Hulubei
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Approximate Formula ◽  
Resonant State ◽  
Global Analysis ◽  
One Dimensional ◽  
Natural Modes ◽  
Resonant States ◽  
Potential Parameters ◽  
Mode A

The natural modes for one-dimensional (1D) twin square potentials of complex strength g are studied. A global analysis of the natural modes based on the construction of the Riemann surfaces RIg and RII g of the multiple valued function k = k(g), where k(g) defines the poles of the transmission coefficient, is done. To each nonradiative or radiative mode a sheet of the Riemann surface is associated. All the natural modes of the system are identified and treated in a unified way. New classes of resonant state poles with exotic properties are identified on the k-plane images of the sheets of RIg and RIIg and the properties of the exotic modes are studied. The traversal time through the 1D twin square potentials is analysed. Subluminal and superluminal traversal times are evidenced. An approximate formula for the frequencies k for which the maximal superluminal velocities are gained as a function of the potential parameters is given.

scholarly journals TRANSCENDENCE OF SPECIAL VALUES OF POCHHAMMER FUNCTIONS

2009 ◽  
Vol 05 (04) ◽  
pp. 667-677
Author(s):  
MARVIN D. TRETKOFF ◽  
PAULA TRETKOFF
Keyword(s):  
Hypergeometric Functions ◽  
Higher Order ◽  
Algebraic Numbers ◽  
Special Values

In this paper, we examine the set of algebraic numbers at which higher order hypergeometric functions take algebraic values. In particular, we deduce criteria for this set to be finite and for it to be infinite.

scholarly journals The higher-order matching polynomial of a graph

2005 ◽  
Vol 2005 (10) ◽  
pp. 1565-1576 ◽  
Author(s):  
Oswaldo Araujo ◽  
Mario Estrada ◽  
Daniel A. Morales ◽  
Juan Rada
Keyword(s):  
Hypergeometric Functions ◽  
Higher Order ◽  
Disjoint Paths ◽  
Hosoya Index ◽  
Matching Polynomial ◽  
Similarities And Differences

Given a graphGwithnvertices, letp(G,j)denote the number of waysjmutually nonincident edges can be selected inG. The polynomialM(x)=∑j=0[n/2](−1)jp(G,j)xn−2j, called the matching polynomial ofG, is closely related to the Hosoya index introduced in applications in physics and chemistry. In this work we generalize this polynomial by introducing the number of disjoint paths of lengtht, denoted bypt(G,j). We compare this higher-order matching polynomial with the usual one, establishing similarities and differences. Some interesting examples are given. Finally, connections between our generalized matching polynomial and hypergeometric functions are found.

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