scholarly journals General soliton and (semi-)rational solutions of the partial reverse space y-non-local Mel’nikov equation with non-zero boundary conditions

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Heming Fu ◽  
Wanshi Lu ◽  
Jiawei Guo ◽  
Chengfa Wu
Keyword(s):  
Boundary Conditions ◽  
Reduction Method ◽  
The Other ◽  
Rational Solutions ◽  
Kp Hierarchy Reduction Method ◽  
Solution Dynamics ◽  
Non Local ◽  
New Feature ◽  
Non Local Equations ◽  
Kp Hierarchy Reduction

General soliton and (semi-)rational solutions to the y-non-local Mel’nikov equation with non-zero boundary conditions are derived by the Kadomtsev–Petviashvili (KP) hierarchy reduction method. The solutions are expressed in N × N Gram-type determinants with an arbitrary positive integer N . A possible new feature of our results compared to previous studies of non-local equations using the KP reduction method is that there are two families of constraints among the parameters appearing in the solutions, which display significant discrepancies. For even N , one of them only generates pairs of solitons or lumps while the other one can give rise to odd numbers of solitons or lumps; the interactions between lumps and solitons are always inelastic for one family whereas the other family may lead to semi-rational solutions with elastic collisions between lumps and solitons. These differences are illustrated by a thorough study of the solution dynamics for N = 1, 2, 3. Besides, regularities of solutions are discussed under proper choices of parameters.

scholarly journals A Novel Dynamic of Localized Solitary Waves for the Hirota-Maccari System

2021 ◽  
Author(s):  
Pei Xia ◽  
Yi Zhang ◽  
Heyan Zhang ◽  
Yindong Zhuang
Keyword(s):  
Solitary Waves ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Dark Solitons ◽  
Kp Hierarchy Reduction Method ◽  
Waves Propagation ◽  
Short Time ◽  
Physical Phenomena ◽  
Localized Waves ◽  
Kp Hierarchy Reduction

Abstract This paper investigates a particular family of semi-rational solutions in determinant form by using the KP hierarchy reduction method, which describe resonant collisions among lumps or resemble line rogue waves and dark solitons in the Hirota-Maccari system. Due to the resonant collisions, the line resemble rogue waves are generated and attenuated in the background of dark solitons with line profiles of finite length, it takes a short time for the lumps to appear from and disappear into the dark solitons background. These novel dynamic of localized solitary waves may be help to understand some physical phenomena of nonlinear localized waves propagation in many physical settings.

Soliton solutions to the nonlocal Davey–Stewartson III equation

2020 ◽  
pp. 2150026
Author(s):  
Heming Fu ◽  
Chenzhen Ruan ◽  
Weiying Hu
Keyword(s):  
Positive Integer ◽  
Reduction Method ◽  
Soliton Solutions ◽  
Regularity Of Solutions ◽  
Kp Hierarchy ◽  
Bilinear Method ◽  
Suitable Parameter ◽  
Kp Hierarchy Reduction Method ◽  
Kp Hierarchy Reduction

The soliton solutions on both constant and periodic backgrounds of the nonlocal Davey–Stewartson III equation are derived by using the bilinear method and the Kadomtsev-Petviashvili (KP) hierarchy reduction method. These solutions are presented as [Formula: see text] Gram-type determinants, with [Formula: see text] a positive integer. Typical dynamics of these soliton solutions are investigated in analytical and graphical aspects. Two types of soliton solutions are generated with different [Formula: see text]. When [Formula: see text] is even, solitons on the constant background can be constructed, whereas solitons appear on the periodic background for odd [Formula: see text]. Under suitable parameter restrictions, we show the regularity of solutions and display all patterns of two- and four-soliton solutions.

scholarly journals Bright-Dark Mixed N-Soliton Solution of Two-Dimensional Multicomponent Maccari System

2017 ◽  
Vol 72 (8) ◽  
pp. 745-755 ◽  
Author(s):  
Zhong Han ◽  
Yong Chen
Keyword(s):  
Soliton Solution ◽  
Reduction Method ◽  
Soliton Solutions ◽  
Two Dimensional ◽  
Kp Hierarchy ◽  
Dark Solitons ◽  
Long Wave ◽  
Special Cases ◽  
Kp Hierarchy Reduction Method ◽  
Kp Hierarchy Reduction

AbstractBased on the KP hierarchy reduction method, we construct the general bright-dark mixed N-soliton solution of the two-dimensional (2D) (M+1)-component Maccari system comprised of M-component short waves (SWs) and one-component long wave (LW) with all possible combinations of nonlinearities. We firstly consider two types of mixed N-soliton solutions (two-bright-one-dark and one-bright-two-dark solitons in SW components) to the (3+1)-component Maccari system in detail. Then by extending our analysis to the (M+1)-component Maccari system, its general m-bright-(M–m)-dark mixed N-soliton solution is obtained. The formula obtained also contains the general all-bright and all-dark N-soliton solutions as special cases. For the two-bright-one-dark mixed soliton solution of the (3+1)-component Maccari system, it can be shown that solioff excitation and solioff interaction take place in the two SW components supporting bright solitons, whereas the SW component supporting dark solitons and the LW component possess V-type solitary and interaction.

scholarly journals An efficient stock market prediction model using hybrid feature reduction method based on variational autoencoders and recursive feature elimination

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Hakan Gunduz
Keyword(s):  
Reduction Method ◽  
Feature Reduction ◽  
The Other ◽  
Recursive Feature Elimination ◽  
Accuracy Rate ◽  
Stock Performance ◽  
Attention Model ◽  
Feature Sets ◽  
Accuracy Rates ◽  
F Measure

AbstractIn this study, the hourly directions of eight banking stocks in Borsa Istanbul were predicted using linear-based, deep-learning (LSTM) and ensemble learning (LightGBM) models. These models were trained with four different feature sets and their performances were evaluated in terms of accuracy and F-measure metrics. While the first experiments directly used the own stock features as the model inputs, the second experiments utilized reduced stock features through Variational AutoEncoders (VAE). In the last experiments, in order to grasp the effects of the other banking stocks on individual stock performance, the features belonging to other stocks were also given as inputs to our models. While combining other stock features was done for both own (named as allstock_own) and VAE-reduced (named as allstock_VAE) stock features, the expanded dimensions of the feature sets were reduced by Recursive Feature Elimination. As the highest success rate increased up to 0.685 with allstock_own and LSTM with attention model, the combination of allstock_VAE and LSTM with the attention model obtained an accuracy rate of 0.675. Although the classification results achieved with both feature types was close, allstock_VAE achieved these results using nearly 16.67% less features compared to allstock_own. When all experimental results were examined, it was found out that the models trained with allstock_own and allstock_VAE achieved higher accuracy rates than those using individual stock features. It was also concluded that the results obtained with the VAE-reduced stock features were similar to those obtained by own stock features.

scholarly journals Replica wormholes for an evaporating 2D black hole

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Kanato Goto ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Path Integral ◽  
Island Rule ◽  
Technical Challenge ◽  
Local Boundary ◽  
Lorentzian Signature ◽  
Special Cases ◽  
Non Local ◽  
Non Local Equations

Abstract Quantum extremal islands reproduce the unitary Page curve of an evaporating black hole. This has been derived by including replica wormholes in the gravitational path integral, but for the transient, evaporating black holes most relevant to Hawking’s paradox, these wormholes have not been analyzed in any detail. In this paper we study replica wormholes for black holes formed by gravitational collapse in Jackiw-Teitelboim gravity, and confirm that they lead to the island rule for the entropy. The main technical challenge is that replica wormholes rely on a Euclidean path integral, while the quantum extremal islands of an evaporating black hole exist only in Lorentzian signature. Furthermore, the Euclidean equations for the Schwarzian mode are non-local, so it is unclear how to connect to the local, Lorentzian dynamics of an evaporating black hole. We address these issues with Schwinger-Keldysh techniques and show how the non-local equations reduce to the local ‘boundary particle’ description in special cases.

Elliptic problem involving non-local boundary conditions

2019 ◽  
Vol 181 ◽  
pp. 87-100
Author(s):  
Noureddine Igbida ◽  
Soma Safimba
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Local Boundary ◽  
Non Local

scholarly journals Unidentified emission features in the R Coronae Borealis star V854 Centauri

2018 ◽  
Vol 610 ◽  
pp. L6 ◽  
Author(s):  
L. C. Oostrum ◽  
B. B. Ochsendorf ◽  
L. Kaper ◽  
A. G. G. M. Tielens
Keyword(s):  
Near Infrared ◽  
Physical Nature ◽  
The Other ◽  
Large Telescope ◽  
Circumstellar Material ◽  
Spatially Resolved ◽  
Broad Emission ◽  
Very Large Telescope ◽  
New Feature ◽  
Molecular Nature

During its 2012 decline, the R Coronae Borealis star (RCB) V854 Cen was spectroscopically monitored with X-shooter on the ESO Very Large Telescope. The obscured optical and near-infrared spectrum exhibits many narrow and several broad emission features, as previously observed. The envelope is spatially resolved along the slit and allows for a detailed study of the circumstellar material. In this Letter, we report on the properties of a number of unidentified visual emission features (UFs), including the detection of a new feature at 8692 Å. These UFs have been observed in the Red Rectangle (RR), but their chemical and physical nature is still a mystery. The previously known UFs behave similarly in the RR and in V854 Cen, but are not detected in six other observed RCBs. Some hydrogen might be required for the formation of their carrier(s). The λ8692 UF is present in all RCBs. Its carrier is likely of a carbonaceous molecular nature, presumably different from that of the other UFs.

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