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Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schr¨odinger equation with sextic operator under non-zero boundary conditions

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Chinese Physics B 2024年第9期33卷 268-280页

作者： Luyao Zhang Xiyang Xie Department of Mathematics and Physics Hebei Key Laboratory of Physics and Energy TechnologyNorth China Electric Power UniversityBaoding 071003China

We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinearSchr¨odinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their *** the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.

关键词： double-pole solitons double-pole breathers Riemann–Hilbert problem non-zero boundary conditions nonlinear Schr¨odinger equation with sextic operator

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ON THE HEAT FLOW OF EQUATION OF H-SURFACE

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Acta Mathematica Scientia 2019年第5期39卷 1397-1405页

作者： Guochun WU Zhong TAN Jiankai XU Fujian Province University Key Laboratory of Computational Science School of Mathematical Sciences Huaqiao University Quanzhou 362021 China School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing Xiamen University Xiamen 361005 China College of Information Science and Technology Hunan Agriculture University Changsha 410128 China

We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique global solution provided the initial data belong to M2 and the global solution converges to zero in H^1 exponentially as time goes to infinity. Moreover, we also prove that the local regular solution must blow up at finite time provided the initial data belong to M1.

关键词： H-surface non-zero Dirichlet boundary singularity global solutions

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Does Entropy Manufacture Impacts DM Density Profiles and How Well Does the Scientific Community Understand If or Not Gravity Is always Either a Classical and/or Quantum Phenomenon at Its Genesis over 13.7 Billion Years Ago?

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Journal of High Energy Physics, Gravitation and Cosmology 2017年第1期3卷 106-137页

作者： Andrew Walcott Beckwith Physics Department College of PhysicsChongqing University Huxi CampusChongqingChina

In the 12th Marcel Grossmann Meeting, July 9th, 2009, the author raised the issue of whether early graviton production could affect non-Gaussian contributions to DM density profiles. Specifically, does a first-order phase transition, in the formation of GW also lead to variation in density fluctuations of space plasma production? and curvature perturbations? We submit that the answer to this question will lead to quantifying fluctuations in space time which affect the stability and formation of DM halos and DM density profiles. Furthermore, we look at whether or not there is a relationship between DM and DE, and gravitons. This is suggested by a modification of Randal Sundrum brane world models, which may be used to admit a very small four-dimensional standard space time non-zero graviton mass. non zero graviton mass in 4 dimensional space time, as well as modification of existing KK graviton theories will lead to a speed-up of cosmological expansion when the red shift was approximately z ≈ 0.5 −0.55, i.e., about a billion years ago. Finally, the issue of if gravity is a quantum phenomenon will be brought up in the context of understanding if or not squeezing of coherent states is mandatory at the onset of inflation.

关键词： KK Graviton Theories non-zero Graviton Mass non-Gaussian Contributions to DM Density Profiles

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A Fermi Energy-Incorporated Framework for Dealing with the Temperature- and Magnetic Field-Dependent Critical Current Densities of Superconductors and Its Application to Bi-2212

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World Journal of Condensed Matter Physics 2020年第2期10卷 53-70页

作者： Gulshan Prakash Malik Vijaya Shankar Varma B-208 Sushant Lok 1 Gurgaon Haryana India 180 Mall Apartments Delhi India

It is well known that the critical current density of a superconductor depends on its size, shape, nature of doping and the manner of preparation. It is suggested here that the collective effect of such differences for different samples of the same superconductor is to endow them with different values of the Fermi energy—a single property to which may be attributed the observed variation in their critical current densities. The study reported here extends our earlier work concerned with the generalized BCS equations [Malik, G.P. (2010) Physica B, 405, 3475-3481;Malik, G.P. (2013) WJCMP, 3,103-110]. We develop here for the first time a framework of microscopic equations that incorporates all of the following parameters of a superconductor: temperature, momentum of Cooper pairs, Fermi energy, applied magnetic field and critical current density. As an application of this framework, we address the different values of critical current densities of Bi-2212 for non-zero values of temperature and applied magnetic field that have been reported in the literature.

关键词： Generalized BCS Equations Fermi Energy Critical Current Density non-zero Temperatures and Applied Fields Bi-2212

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