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Soliton Management for ultrashort pulse: dark and anti-dark solitons of Fokas-Lenells equation with a damping like perturbation and a gauge equivalent spin system 超短脉冲的孤子管理：具有类似阻尼扰动的 Fokas-Lenells 方程的暗孤子和反暗孤子以及等价自旋系统
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-06 DOI: arxiv-2402.03831
Riki Dutta, Gautam K Saharia, Sagardeep Talukdar, Sudipta Nandy
{"title":"Soliton Management for ultrashort pulse: dark and anti-dark solitons of Fokas-Lenells equation with a damping like perturbation and a gauge equivalent spin system","authors":"Riki Dutta, Gautam K Saharia, Sagardeep Talukdar, Sudipta Nandy","doi":"arxiv-2402.03831","DOIUrl":"https://doi.org/arxiv-2402.03831","url":null,"abstract":"We investigate the propagation of an ultrashort optical pulse using\u0000Fokas-Lenells equation (FLE) under varying dispersion, nonlinear effects and\u0000perturbation. Such a system can be said to be under soliton management (SM)\u0000scheme. At first, under a gauge transformation, followed by shifting of\u0000variables, we transform FLE under SM into a simplified form, which is similar\u0000to an equation given by Davydova and Lashkin for plasma waves, we refer to this\u0000form as DLFLE. Then, we propose a bilinearization for DLFLE in a non-vanishing\u0000background by introducing an auxiliary function which transforms DLFLE into\u0000three bilinear equations. We solve these equations and obtain dark and\u0000anti-dark one-soliton solution (1SS) of DLFLE. From here, by reverse\u0000transformation of the solution, we obtain the 1SS of FLE and explore the\u0000soliton behavior under different SM schemes. Thereafter, we obtain dark and\u0000anti-dark two-soliton solution (2SS) of DLFLE and determine the shift in phase\u0000of the individual solitons on interaction through asymptotic analysis. We then,\u0000obtain the 2SS of FLE and represent the soliton graph for different SM scheme.\u0000Thereafter, we present the procedure to determine N-soliton solution (NSS) of\u0000DLFLE and FLE. Later, we introduce a Lax pair for DLFLE and through a gauge\u0000transformation we convert the spectral problem of our system into that of an\u0000equivalent spin system which is termed as Landau-Lifshitz (LL) system. LL\u0000equation (LLE) holds the potential to provide information about various\u0000nonlinear structures and properties of the system.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760218","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
The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint 开放的 XYZ 自旋 1/2 链：边界场的变量分离和标量乘积的约束关系
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-06 DOI: arxiv-2402.04112
G. Niccoli, V. Terras
{"title":"The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint","authors":"G. Niccoli, V. Terras","doi":"arxiv-2402.04112","DOIUrl":"https://doi.org/arxiv-2402.04112","url":null,"abstract":"We consider the open XYZ spin chain with boundary fields. We solve the model\u0000by the new Separation of Variables approach introduced in arXiv:1904.00852. In\u0000this framework, the transfer matrix eigenstates are obtained as a particular\u0000sub-class of the class of so-called separate states. We consider the problem of\u0000computing scalar products of such separate states. As usual, they can be\u0000represented as determinants with rows labelled by the inhomogeneity parameters\u0000of the model. We notably focus on the special case in which the boundary\u0000parameters parametrising the two boundary fields satisfy one constraint, hence\u0000enabling for the description of part of the transfer matrix spectrum and\u0000eigenstates in terms of some elliptic polynomial Q-solution of a usual\u0000TQ-equation. In this case, we show how to transform the aforementioned\u0000determinant for the scalar product into some more convenient form for the\u0000consideration of the homogeneous and thermodynamic limits: as in the open XXX\u0000or XXZ cases, our result can be expressed as some generalisation of the\u0000so-called Slavnov determinant.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760317","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
On the integrability of spinning-body dynamics around black holes 论黑洞周围旋转体动力学的可积分性
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-05 DOI: arxiv-2402.02670
Paul Ramond
{"title":"On the integrability of spinning-body dynamics around black holes","authors":"Paul Ramond","doi":"arxiv-2402.02670","DOIUrl":"https://doi.org/arxiv-2402.02670","url":null,"abstract":"In general relativity, the trajectory of a celestial body in a given\u0000spacetime is influenced by its proper rotation, or textit{spin}. We present a\u0000covariant and physically self-consistent Hamiltonian framework to study this\u0000motion, at linear order in the body's spin and in an arbitrary fixed spacetime.\u0000The choice of center-of-mass and degeneracies coming from Lorentz invariance\u0000are treated rigorously with adapted tools from Hamiltonian mechanics. Applying\u0000the formalism to a background space-time described by the Kerr metric, we prove\u0000that the motion of a spinning body around a generic rotating black hole is an\u0000textit{integrable} Hamiltonian system. In particular, linear-in-spin effects\u0000do not break the integrability of Kerr geodesics, and induce no textit{chaos}\u0000within the associated phase space. Our findings suggest a natural way to\u0000improve current gravitational waveform modelling for asymmetric binary systems,\u0000and provide a mean to extend classical features of Kerr geodesics to\u0000linear-in-spin trajectories.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760395","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
The Lax pairs and conserved quantities of the delay Lotka-Volterra equation 延迟洛特卡-伏特拉方程的拉克斯对和守恒量
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-03 DOI: arxiv-2402.02204
Hiroshi Matsuoka, Kenta Nakata, Ken-ichi Maruno
{"title":"The Lax pairs and conserved quantities of the delay Lotka-Volterra equation","authors":"Hiroshi Matsuoka, Kenta Nakata, Ken-ichi Maruno","doi":"arxiv-2402.02204","DOIUrl":"https://doi.org/arxiv-2402.02204","url":null,"abstract":"The delay Lotka-Volterra equation is a delay-differential extension of the\u0000well known Lotka-Volterra equation, and is known to have N-soliton solutions.\u0000In this paper, Backlund transformations, Lax pairs and infinite conserved\u0000quantities of the delay Lotka-Volterra equation and its discrete analogue are\u0000constructed. The conserved quantities of the delay Lotka-Volterra equation turn\u0000out to be complicated and described by using the time-ordered product of linear\u0000operators.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760318","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
Defocusing Hirota equation with fully asymmetric non-zero boundary conditions: the inverse scattering transform 具有完全非对称非零边界条件的广田散焦方程：反向散射变换
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-01-30 DOI: arxiv-2401.16684
Rusuo Ye, Peng-Fei Han, Yi Zhang
{"title":"Defocusing Hirota equation with fully asymmetric non-zero boundary conditions: the inverse scattering transform","authors":"Rusuo Ye, Peng-Fei Han, Yi Zhang","doi":"arxiv-2401.16684","DOIUrl":"https://doi.org/arxiv-2401.16684","url":null,"abstract":"The paper aims to apply the inverse scattering transform to the defocusing\u0000Hirota equation with fully asymmetric non-zero boundary conditions (NZBCs),\u0000addressing scenarios in which the solution's limiting values at spatial\u0000infinities exhibit distinct non-zero moduli. In comparison to the symmetric\u0000case, we explore the characteristic branched nature of the relevant scattering\u0000problem explicitly, instead of introducing Riemann surfaces. For the direct\u0000problem, we formulate the Jost solutions and scattering data on a single sheet\u0000of the scattering variables. We then derive their analyticity behavior,\u0000symmetry properties, and the distribution of discrete spectrum. Additionally,\u0000we study the behavior of the eigenfunctions and scattering data at the branch\u0000points. Finally, the solutions to the defocusing Hirota equation with\u0000asymmetric NZBCs are presented through the related Riemann-Hilbert problem on\u0000an open contour. Our results can be applicable to the study of asymmetric\u0000conditions in nonlinear optics.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139645637","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
Yang--Baxter maps of KdV, NLS and DNLS type on division rings 划分环上的 KdV、NLS 和 DNLS 型杨--巴克斯特映射
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-01-29 DOI: arxiv-2401.16485
S. Konstantinou-Rizos, A. A. Nikitina
{"title":"Yang--Baxter maps of KdV, NLS and DNLS type on division rings","authors":"S. Konstantinou-Rizos, A. A. Nikitina","doi":"arxiv-2401.16485","DOIUrl":"https://doi.org/arxiv-2401.16485","url":null,"abstract":"We construct nocommutative set-theoretical solutions to the Yang--Baxter\u0000equation related to the KdV, the NLS and the derivative NLS equations. In\u0000particular, we construct several Yang--Baxter maps of KdV type and we show that\u0000one of them is completely integrable in the Liouville sense. Then, we construct\u0000a noncommutative KdV type Yang--Baxter map which can be squeezed down to the\u0000noncommutative discrete potential KdV equation. Moreover, we construct Darboux\u0000transformations for the noncommutative derivative NLS equation. Finally, we\u0000consider matrix refactorisation problems for noncommutative Darboux matrices\u0000associated with the NLS and the derivative NLS equation and we construct\u0000noncommutative maps. We prove that the latter are solutions to the Yang--Baxter\u0000equation.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139645018","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
Visualisation of counter-rotating dust disks using ray tracing methods 利用光线追踪方法实现逆旋转尘埃盘的可视化
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-01-21 DOI: arxiv-2401.11498
Eddy B. de Leon, J. Frauendiener, C. Klein
{"title":"Visualisation of counter-rotating dust disks using ray tracing methods","authors":"Eddy B. de Leon, J. Frauendiener, C. Klein","doi":"arxiv-2401.11498","DOIUrl":"https://doi.org/arxiv-2401.11498","url":null,"abstract":"A detailed study of ray tracing in the space-time generated by a disk of\u0000counter-rotating dust is presented. The space-time is given in explicit form in\u0000terms of hyperelliptic theta functions. The numerical approach to ray tracing\u0000is set up for general stationary axisymmetric space-times and tested at the\u0000well-studied example of the Kerr solution. Similar features as in the case of a\u0000rotating black hole, are explored in the case of a dust disk. The effect of the central redshift varying between a Newtonian disk and the\u0000ultrarelativistic disk, where the exterior of the disk can be interpreted as\u0000the extreme Kerr solution, and the transition from a single component disk to a\u0000static disk is explored. Frame dragging, as well as photon spheres, are\u0000discussed.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139559756","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
Integrable nonlocal finite-dimensional Hamiltonian systems related to the Ablowitz-Kaup-Newell-Segur system 与阿布罗维茨-考普-纽维尔-塞古尔系统相关的可积分非局部有限维哈密顿系统
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-01-20 DOI: arxiv-2401.11259
Baoqiang Xia, Ruguang Zhou
{"title":"Integrable nonlocal finite-dimensional Hamiltonian systems related to the Ablowitz-Kaup-Newell-Segur system","authors":"Baoqiang Xia, Ruguang Zhou","doi":"arxiv-2401.11259","DOIUrl":"https://doi.org/arxiv-2401.11259","url":null,"abstract":"The method of nonlinearization of the Lax pair is developed for the\u0000Ablowitz-Kaup-Newell-Segur (AKNS) equation in the presence of space-inverse\u0000reductions. As a result, we obtain a new type of finite-dimensional Hamiltonian\u0000systems: they are nonlocal in the sense that the inverse of the space variable\u0000is involved. For such nonlocal Hamiltonian systems, we show that they preserve\u0000the Liouville integrability and they can be linearized on the Jacobi variety.\u0000We also show how to construct the algebro-geometric solutions to the AKNS\u0000equation with space-inverse reductions by virtue of our nonlocal\u0000finite-dimensional Hamiltonian systems. As an application, algebro-geometric\u0000solutions to the AKNS equation with the Dirichlet and with the Neumann boundary\u0000conditions, and algebro-geometric solutions to the nonlocal nonlinear\u0000Schr\"{o}dinger (NLS) equation are obtained.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139559593","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
Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems 保守哈密顿系统中凝结现象一致性的精确解
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-01-18 DOI: arxiv-2401.15083
Anxo Biasi
{"title":"Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems","authors":"Anxo Biasi","doi":"arxiv-2401.15083","DOIUrl":"https://doi.org/arxiv-2401.15083","url":null,"abstract":"While it is known that Hamiltonian systems may undergo a phenomenon of\u0000condensation akin to Bose-Einstein condensation, not all the manifestations of\u0000this phenomenon have been uncovered yet. In this work, we present a novel form\u0000of condensation in conservative Hamiltonian systems, which happens through\u0000coherent states and exploits the discreteness of our system. Both features\u0000markedly differ from well-known condensation processes in the literature. Our\u0000result is based on a deterministic approach to obtain exact explicit solutions\u0000representing the dynamical formation of condensates in finite time. We reveal a\u0000dual-cascade behavior during the process, featuring inverse and direct transfer\u0000of conserved quantities across the spectrum. The direct cascade yields the\u0000excitation of high modes in finite time, a phenomenon quantified through the\u0000blow-up of Sobolev norms. We provide a fully analytic description of all the\u0000processes involved.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139645024","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
Bilinear expansions of KP multipair correlators in BKP correlators BKP 相关器中 KP 多对相关器的双线性展开
arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-01-11 DOI: arxiv-2401.06032
J. Harnad, A. Yu. Orlov
{"title":"Bilinear expansions of KP multipair correlators in BKP correlators","authors":"J. Harnad, A. Yu. Orlov","doi":"arxiv-2401.06032","DOIUrl":"https://doi.org/arxiv-2401.06032","url":null,"abstract":"In earlier work, Schur lattices of KP and BKP $tau$-functions, denoted\u0000$pi_{lambda}(g) ({bf t})$ and $kappa_{alpha} (h)({bf t}_B)$,\u0000respectively, defined as fermionic vacuum expectation values, were associated\u0000to every GL$(infty)$ group element $hat{g}$ and SO$(tilde{mathcal{H}}^pm,\u0000Q_pm)$ group element $hat{h}$. The elements of these lattices are labelled by\u0000partitions $lambda$ and strict partitions $alpha$, respectively. It was shown\u0000how the former may be expressed as finite bilinear sums over products of the\u0000latter. In this work, we show that two-sided KP tau functions corresponding to\u0000any given $hat{g}$ may similarly be expressed as bilinear combinations of the\u0000corresponding two-sided BKP tau functions.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139462457","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
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