scholarly journals Approximate Symmetries of the Harry Dym Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Mehdi Nadjafikhah ◽  
Parastoo Kabi-Nejad
Keyword(s):  
Lie Algebra ◽  
Optimal System ◽  
Differential Invariants ◽  
Approximate Symmetries ◽  
One Dimensional ◽  
First Order ◽  
Optimal System Of Subalgebras ◽  
Dym Equation ◽  
The One ◽  
Harry Dym Equation

We derive the first-order approximate symmetries for the Harry Dym equation by the method of approximate transformation groups proposed by Baikov et al. (1989, 1996). Moreover, we investigate the structure of the Lie algebra of symmetries of the perturbed Harry Dym equation. We compute the one-dimensional optimal system of subalgebras as well as point out some approximately differential invariants with respect to the generators of Lie algebra and optimal system.

scholarly journals Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds

2020 ◽  
Vol 8 (1) ◽  
pp. 68-91
Author(s):  
Gianmarco Giovannardi
Keyword(s):  
Characteristic Direction ◽  
Fixed Degree ◽  
One Dimensional ◽  
First Order ◽  
Natural Choice ◽  
Higher Dimensional ◽  
Graded Manifold ◽  
The One ◽  
Graded Manifolds ◽  
Holonomy Map

AbstractThe deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a notion of higher dimensional holonomy map in analogy with the one-dimensional case [29], and we provide a characterization for singularities as well as a deformability criterion.

scholarly journals SYMMETRY ANALYSIS OF TELEGRAPH EQUATION

2011 ◽  
Vol 04 (01) ◽  
pp. 117-126
Author(s):  
Mehdi Nadjafikhah ◽  
Seyed-Reza Hejazi
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Telegraph Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Group Method ◽  
Parameter Group ◽  
One Dimensional

Lie symmetry group method is applied to study the telegraph equation. The symmetry group and one-parameter group associated to the symmetries with the structure of the Lie algebra symmetries are determined. The reduced version of equation and its one-dimensional optimal system are given.

scholarly journals A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function

2002 ◽  
Vol 65 (2) ◽  
pp. 253-258 ◽  
Author(s):  
Hitoshi Tanaka
Keyword(s):  
Sobolev Space ◽  
Maximal Function ◽  
60Th Birthday ◽  
One Dimensional ◽  
Partial Derivatives ◽  
First Order ◽  
Littlewood Maximal Function ◽  
The One ◽  
Derivatives Of

Dedicated to Professor Kôzô Yabuta on the occasion of his 60th birthdayJ. Kinnunen proved that of P > 1, d ≤ 1 and f is a function in the Sobolev space W1,P(Rd), then the first order weak partial derivatives of the Hardy-Littlewood maximal function ℳf belong to LP(Rd). We shall show that, when d = 1, Kinnunen's result can be extended to the case where P = 1.

scholarly journals Extended Conformal Symmetry of the One-Dimensional Bose Gas

1997 ◽  
Vol 12 (29) ◽  
pp. 2153-2159 ◽  
Author(s):  
Milena Maule ◽  
Stefano Sciuto
Keyword(s):  
Cartan Subalgebra ◽  
Conformal Symmetry ◽  
Hard Core ◽  
Bose Gas ◽  
Effective Hamiltonian ◽  
Coupling Constant ◽  
Free Fermions ◽  
One Dimensional ◽  
First Order ◽  
The One

We show that the low-lying excitations of the one-dimensional Bose gas are described, at all orders in a 1/N expansion and at the first order in the inverse of the coupling constant, by an effective Hamiltonian written in terms of an extended conformal algebra, namely the Cartan subalgebra of the [Formula: see text] algebra. This enables us to construct the first interaction term which corrects the Hamiltonian of the free fermions equivalent to a hard-core boson system.

scholarly journals Non-unitary dynamics of Sachdev-Ye-Kitaev chain

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Chunxiao Liu ◽  
Pengfei Zhang ◽  
Xiao Chen
Keyword(s):  
Conformal Symmetry ◽  
Entangled State ◽  
One Dimensional ◽  
First Order ◽  
Large N ◽  
First Order Phase Transition ◽  
Free Fermion Model ◽  
Kitaev Model ◽  
The One ◽  
First Order Phase

We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large N limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.

One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Classification Problem ◽  
Singularity Analysis ◽  
Optimal System ◽  
One Dimensional ◽  
Infinitesimal Generators ◽  
Similarity Transformations ◽  
Painlevé Property ◽  
Point Transformations ◽  
Travel Wave ◽  
The One

Abstract We apply the Lie theory to determine the infinitesimal generators of the one-parameter point transformations which leave invariant the 3 + 1 Kudryashov–Sinelshchikov equation. We solve the classification problem of the one-dimensional optimal system, while we derive all the possible independent Lie invariants; that is, we determine all the independent similarity transformations which lead to different reductions. For an application, the results are applied to prove the existence of travel-wave solutions. Furthermore, the method of singularity analysis is applied where we show that the 3 + 1 Kudryashov–Sinelshchikov equation possess the Painlevé property and its solution can be written by using a Laurent expansion.

scholarly journals THE EFFECT OF OFF-RAMP ON THE ONE-DIMENSIONAL CELLULAR AUTOMATON TRAFFIC FLOW WITH OPEN BOUNDARIES

2004 ◽  
Vol 18 (16) ◽  
pp. 2347-2360 ◽  
Author(s):  
HAMID EZ-ZAHRAOUY ◽  
ZOUBIR BENRIHANE ◽  
ABDELILAH BENYOUSSEF
Keyword(s):  
Cellular Automaton ◽  
Traffic Flow ◽  
Average Density ◽  
Constant Current ◽  
Current Phase ◽  
One Dimensional ◽  
First Order ◽  
Open Boundaries ◽  
Flow Phase ◽  
The One

The effect of the position of the off-ramp (way out), on the traffic flow phase transition is investigated using numerical simulations in the one-dimensional cellular automaton traffic flow model with open boundaries using parallel dynamics. When the off-ramp is located between two critical positions ic1 and ic2 the current increases with the extracting rate β0, for β0<β0c1, and exhibits a plateau (constant current) for β0c1<β0<β0c2 and decreases with β0 for β0>β0c2. However, the density undergoes two successive first order transitions: from high density to plateau current phase at β0=β0c1; and from average density to the low one at β0=β0c2. In the case of two off-ramps located respectively at i1 and i2, these transitions occur only when i2-i1 is smaller than a critical value. Phase diagrams in the (α,β0), (β,β0) and (i1,β0) planes are established. It is found that the transitions between free traffic (FT), congested traffic (CT) and plateau current (PC) phases are of first order. The first order line transition in (i1,β0)-phase diagram terminates by an end point above which the transition disappears.

TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A CHEREDNIK TYPE OPERATOR ON THE REAL LINE

2010 ◽  
Vol 08 (04) ◽  
pp. 387-408 ◽  
Author(s):  
MOHAMED ALI MOUROU
Keyword(s):  
Real Line ◽  
Difference Operators ◽  
Generalized Convolution ◽  
One Dimensional ◽  
The Real ◽  
First Order ◽  
Wiener Theorem ◽  
The Fourier Transform ◽  
The One ◽  
Transmutation Operators

We consider a singular differential-difference operator Λ on the real line which generalizes the one-dimensional Cherednik operator. We construct transmutation operators between Λ and first-order regular differential-difference operators on ℝ. We exploit these transmutation operators, firstly to establish a Paley–Wiener theorem for the Fourier transform associated with Λ, and secondly to introduce a generalized convolution on ℝ tied to Λ.

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