Journal of Physics A: Mathematical and Theoretical最新文献_第7页

Erratum: Asymptotic expansions for field moments of bound states (2023 J. Phys. A: Math. Theor. 56 244001) 勘误：束缚态场矩的渐近展开（2023 J. Phys. A: Math. Theor. 56 244001）

Journal of Physics A: Mathematical and Theoretical Pub Date : 2023-11-10 DOI: 10.1088/1751-8121/ad0833

G. Forbes, Miguel A Alonso

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Transposed Poisson structures on solvable and perfect Lie algebras 可解和完备李代数上的变换泊松结构

Journal of Physics A: Mathematical and Theoretical Pub Date : 2023-10-01 DOI: 10.1088/1751-8121/ad1620

I. Kaygorodov, A. Khudoyberdiyev

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Domain walls and vector solitons in the coupled nonlinear Schrödinger equation 耦合非线性薛定谔方程中的域墙和矢量孤子

Journal of Physics A: Mathematical and Theoretical Pub Date : 2023-08-28 DOI: 10.1088/1751-8121/ad1622

David D. J. M. Snee, Yi-ping Ma

{"title":"Domain walls and vector solitons in the coupled nonlinear Schrödinger equation","authors":"David D. J. M. Snee, Yi-ping Ma","doi":"10.1088/1751-8121/ad1622","DOIUrl":"https://doi.org/10.1088/1751-8121/ad1622","url":null,"abstract":"We outline a program to classify domain walls (DWs) and vector solitons in the 1D two-component coupled nonlinear Schrödinger (CNLS) equation without restricting the signs or magnitudes of any coeﬃcients. The CNLS equation is reduced ﬁrst to a complex ordinary diﬀerential equation (ODE), and then to a real ODE after imposing a restriction. In the real ODE, we identify four possible equilibria including ZZ, ZN, NZ, and NN, with Z (N) denoting a zero (nonzero) value in a component, and analyze their spatial stability. We identify two types of DWs including asymmetric DWs between ZZ and NN and symmetric DWs between ZN and NZ. We identify three codimension-1 mechanisms for generating vector solitons in the real ODE including heteroclinic cycles, local bifurcations, and exact solutions. Heteroclinic cycles are formed by assembling two DWs back-to-back and generate extended bright-bright (BB), dark-dark (DD), and dark-bright (DB) solitons. Local bifurcations include the Turing (Hamiltonian-Hopf) bifurcation that generates Turing solitons with oscillatory tails and the pitchfork bifurcation that generates DB, bright-antidark, DD, and dark-antidark solitons with monotonic tails. Exact solutions include scalar bright and dark solitons with vector amplitudes. Any codimension-1 real vector soliton can be numerically continued into a codimension-0 family. Complex vector solitons have two more parameters: a dark or antidark component can be numerically continued in the wavenumber, while a bright component can be multiplied by a constant phase factor. We introduce a numerical continuation method to ﬁnd real and complex vector solitons and show that DWs and DB solitons in the immiscible regime can be related by varying bifurcation parameters. We show that collisions between two DB solitons with a nonzero phase diﬀerence in their bright components typically feature a mass exchange that changes the frequencies and phases of the two bright components and the two soliton velocities.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139348676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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The Havriliak–Negami and Jurlewicz–Weron–Stanislavsky relaxation models revisited: memory functions based study 哈夫里利亚克-涅伽米和尤尔列维茨-韦龙-斯坦尼斯拉夫斯基松弛模型再探讨：基于记忆功能的研究

Journal of Physics A: Mathematical and Theoretical Pub Date : 2023-06-19 DOI: 10.1088/1751-8121/acdf9b

K. Górska, A. Horzela, K. Penson

{"title":"The Havriliak–Negami and Jurlewicz–Weron–Stanislavsky relaxation models revisited: memory functions based study","authors":"K. Górska, A. Horzela, K. Penson","doi":"10.1088/1751-8121/acdf9b","DOIUrl":"https://doi.org/10.1088/1751-8121/acdf9b","url":null,"abstract":"We provide a review of theoretical results concerning the Havriliak–Negami (HN) and the Jurlewicz–Weron–Stanislavsky (JWS) dielectric relaxation models. We derive explicit forms of functions characterizing relaxation phenomena in the time domain—the relaxation, response and probability distribution functions. We also explain how to construct and solve relevant evolution equations within these models. These equations are usually solved by using the Schwinger parametrization and the integral transforms. Instead, in this work we replace it by the powerful Efros theorem. That allows one to relate physically admissible solutions to the memory-dependent evolution equations with phenomenologically known spectral functions and, from the other side, with the subordination mechanism emerging from a stochastic analysis of processes underpinning considered relaxation phenomena. Our approach is based on a systematic analysis of the memory-dependent evolution equations. It exploits methods of integral transforms, operational calculus and special functions theory with the completely monotone and Bernstein functions. Merging analytic and stochastic methods enables us to give a complete classification of the standard functions used to describe the large class of the relaxation phenomena and to explain their properties.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139369442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0