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Nonisospectral equations from the Cauchy matrix approach 从考奇矩阵方法看非谱方程
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00055-7
{"title":"Nonisospectral equations from the Cauchy matrix approach","authors":"","doi":"10.1016/S0034-4877(24)00055-7","DOIUrl":"10.1016/S0034-4877(24)00055-7","url":null,"abstract":"<div><div>The Cauchy matrix approach is developed to construct explicit solutions for some nonisospectral equations, including the nonisospectral Korteweg–de Vries (KdV) equation, the nonisospectral modified KdV equation, and the nonisospectral sine-Gordon equation. By means of a Sylvester equation, a set of scalar master functions {<em>S</em><sup>(<em>i,j</em>)</sup>} is defined. We show how nonisospectral dispersion relations are introduced such that the evolutions of {<em>S</em><sup>(<em>i,j</em>)</sup>} can be derived. Some identities of {<em>S</em><sup>(<em>i,j</em>)</sup>} are employed in verifying solutions. Some explicit one-soliton and two-soliton solutions are illustrated together with analysis of their dynamics.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New solutions of the lattice Kadomtsev–Petviashvili system associated with an elliptic curve 与椭圆曲线相关的卡多姆采夫-彼得维亚什维利晶格系统的新解
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00053-3
{"title":"New solutions of the lattice Kadomtsev–Petviashvili system associated with an elliptic curve","authors":"","doi":"10.1016/S0034-4877(24)00053-3","DOIUrl":"10.1016/S0034-4877(24)00053-3","url":null,"abstract":"<div><div>A generalization of the lattice Kadomtsev–Petviashvili system associated with an elliptic curve, that is referred to as an elliptic integrable system, has been revisited by means of the Cauchy matrix scheme. Various types of explicit solutions are obtained, some of which offer new insights of both mathematical and physical significance. The construction of exact solutions to the elliptic lattice Kadomtsev–Petviashvili system is closely connected to that of a special Sylvester-type matrix equation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Certain advancements in multidimensional q-hermite polynomials 多维q-hermite多项式的若干进展
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00059-4
{"title":"Certain advancements in multidimensional q-hermite polynomials","authors":"","doi":"10.1016/S0034-4877(24)00059-4","DOIUrl":"10.1016/S0034-4877(24)00059-4","url":null,"abstract":"<div><div>In the realm of specialized functions, the allure of <em>q</em>-calculus beckons to many scholars, captivating them with its prowess in shaping models of quantum computing, noncommutative probability, combinatorics, functional analysis, mathematical physics, approximation theory, and beyond. This study explores a new idea called the multidimensional <em>q</em>-Hermite polynomials, using different <em>q</em>-calculus techniques. Numerous properties and novel findings regarding these polynomials are derived, encompassing their generating function, series representations, recurrence relations, <em>q</em>-differential formula, and operational principles. Further, we proved that these polynomials are quasi-monomial in <em>q</em>-aspect. As the applications, these findings are subsequently employed to address connection between the multidimensional <em>q</em>-Hermite polynomials and the two-variable <em>q</em>-Legendre polynomials for the first time. Various characterizations are examined, as well the graphical representations of the two-variable <em>q</em>-Legendre polynomials are provided by the surface plots and graphs of distribution of zeros for the <em>q</em>-Legendre polynomials with some specific set of parameters are shown using Mathematica. Our investigations shed light on the intricate nature of these polynomials, elucidating their behaviour and facilitating deeper understanding within the realm of <em>q</em>-calculus.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weakly periodic gibbs measures for the HC model with a countable set of spin values 具有可数自旋值集的 HC 模型的弱周期吉布斯量度
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00057-0
{"title":"Weakly periodic gibbs measures for the HC model with a countable set of spin values","authors":"","doi":"10.1016/S0034-4877(24)00057-0","DOIUrl":"10.1016/S0034-4877(24)00057-0","url":null,"abstract":"<div><div>In this paper, we study the weakly periodic (nonperiodic) Gibbs measures for the Hard Core (HC) model with a countable set ℤ of spin values and with a countable set of parameters <em>λ<sub>i</sub> &gt;</em> 0, <em>i</em> ∈ ℤ, on a Cayley tree of order <em>k</em> ≥ 2. For the considered model in the case ∑<em><sub>i</sub></em> λ<em><sub>i</sub></em> &lt; +∞, a complete description of weakly periodic Gibbs measures is obtained for any normal divisor of index two and in the case ∑<em><sub>i</sub></em>; λ<em><sub>i</sub></em> = +∞, it is shown that there is no weakly periodic Gibbs measure. Moreover, in the case of a normal divisor of index four the uniqueness conditions for weakly periodic Gibbs measures are found. Further, under certain conditions an exact critical value is found that ensures the existence of weakly periodic Gibbs measures.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Construction of quadratic invariants for time-dependent systems in complex phase space using Struckmeier and Riedel approach 用斯特拉克迈尔和里德尔方法构建复相空间时变系统的二次不变量
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00052-1
{"title":"Construction of quadratic invariants for time-dependent systems in complex phase space using Struckmeier and Riedel approach","authors":"","doi":"10.1016/S0034-4877(24)00052-1","DOIUrl":"10.1016/S0034-4877(24)00052-1","url":null,"abstract":"<div><div>In this paper, we deal with the construction of quadratic invariants in a complex phase space under the transformation <em>z</em> = (<em>x</em> + <em>iy</em>) and\u0000<span><math><mrow><mover><mi>z</mi><mo>¯</mo></mover><mo>=</mo><mrow><mo>(</mo><mrow><mi>x</mi><mo>-</mo><mi>i</mi><mi>y</mi></mrow><mo>)</mo></mrow></mrow></math></span> for various time-dependent systems. For this purpose, Struckmeier and Riedel (SR) approach [<span><span>1</span></span>, <span><span>2</span></span>] is used. The constructed invariants include an unknown function <em>f</em><sub>2</sub>(<em>t</em>) that is a solution of a third-order differential equation and its coefficients can be determined by the trajectories of the particle. The invariants play an important role in the study of a dynamical system, to access the accuracy in numerical simulations and to investigate the classical and quantum integrability of a system.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher-order squeezing of both quadrature components in superposition of orthogonal even coherent state and vacuum state 正交偶相干态和真空态叠加时两个正交分量的高阶挤压
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00056-9
{"title":"Higher-order squeezing of both quadrature components in superposition of orthogonal even coherent state and vacuum state","authors":"","doi":"10.1016/S0034-4877(24)00056-9","DOIUrl":"10.1016/S0034-4877(24)00056-9","url":null,"abstract":"<div><div>We study the Hong–Mandel higher-order squeezing of both quadrature components for an arbitrary 2<em>n</em><sup>th</sup>-order (<em>n</em> ≠1) considering the most general Hermitian operator, <em>X<sub>θ</sub> = X</em><sub>1</sub> cos <em>θ + iX</em><sub>2</sub> sin <em>θ</em>, in the superposed state, |<em>Ψ</em>〉 = <em><strong>K</strong></em> [|Ψ<sub>0</sub>) + <em>re</em><sup><em>i</em>ϕ</sup> |0〉] of the orthogonal even coherent state and vacuum state. Here | Ψ<sub>0</sub>〉 = <strong><em>K</em></strong>[|α, +〉 + |iα, +〉] is the orthogonal coherent state, |α, +〉 = <strong><em>K</em></strong>′[|α) + | – α〉] and |<em>i</em>α, +〉 = <strong><em>K</em></strong><em>″</em> [|<em>i</em>α, +〉 + | – <em>i</em>α, +〉] are even coherent states, operators <em>X</em><sub>1,2</sub> are defined by <em>X</em><sub>1</sub> + <em>iX</em><sub>2</sub> = <em>a, a</em> is the annihilation operator, α, <em>θ</em>, <em>r</em> and ϕ are arbitrary parameters and the only restriction on these is the normalization condition of the superposed state |<em>Ψ</em>〉. We find that maximum simultaneous 2<em>n</em><sup>th</sup>-order Hong–Mandel squeezing of both quadrature components <em>X<sub>θ</sub></em> and <em>X<sub>θ+π</sub></em>/2 exhibited by the orthogonal even coherent state enhances in its superposition with vacuum state. We conclude that the values of higher-order momenta in the superposed state become much closer to the best minimum values of the corresponding values of higher-order momenta explored numerically so far than that obtained in orthogonal even coherent state. Variations of 2<em>n</em><sup>th</sup>-order squeezing for <em>n</em> = 2,3 and 4, i.e. fourth, sixth and eighth-order squeezing with different parameters have also been discussed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on almost pseudo symmetric spacetimes with certain application to f(R), gravity 关于几乎伪对称时空的说明，以及对 f(R)、引力的某些应用
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00054-5
{"title":"A note on almost pseudo symmetric spacetimes with certain application to f(R), gravity","authors":"","doi":"10.1016/S0034-4877(24)00054-5","DOIUrl":"10.1016/S0034-4877(24)00054-5","url":null,"abstract":"<div><div>This article deals with the characterization of an almost pseudo symmetric spacetime and we illustrate that a conformally flat almost pseudo symmetric spacetime with nonzero constant scalar curvature represents a perfect fluid spacetime. Also, it is established that the chosen spacetime represents a spacetime of quasi constant sectional curvature and generalized Robertson-Walker spacetime. Besides, we find under what condition the spacetime represents radiation era and dust matter fluid. Further it is shown that under certain restriction in an almost pseudo symmetric spacetime, if the Ricci tensor is Killing, then it represents a static spacetime and it is vacuum. Lastly, we study the impact of this spacetime under <em>f</em>(<em>R)</em> gravity scenario and deduce several energy conditions.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New operator realization of angular momentum for description of electron's motion in uniform magnetic field 描述电子在匀强磁场中运动的角动量新算子实现方法
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1016/S0034-4877(24)00058-2
{"title":"New operator realization of angular momentum for description of electron's motion in uniform magnetic field","authors":"","doi":"10.1016/S0034-4877(24)00058-2","DOIUrl":"10.1016/S0034-4877(24)00058-2","url":null,"abstract":"<div><div>By introducing appropriate electron's coordinate eigenstate and momentum eigenstate we propose new realization of angular momentum operators for describing electron's motion in uniform magnetic field. The coordinate eigenstates make up a representation and embody quantum entanglement between magnetic field and electron. The eigenstate of angular momentum's lowering-ascending operator <strong><em>L</em><sub>±</sub></strong> are derived, the way we tackle this problem is to make an analogue between the transform\u0000<span><math><mrow><msup><mi>e</mi><mrow><mn>2</mn><mi>f</mi><msub><mi>L</mi><mi>z</mi></msub></mrow></msup><msub><mi>L</mi><mo>±</mo></msub><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>f</mi><msub><mi>L</mi><mi>z</mi></msub></mrow></msup></mrow></math></span> to the squeezing mechanism. All these discussions reveal that the quantum theory for charged particles' motion in magnetic field needs to be developed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A combined derivative nonlinear SchrÖdinger soliton hierarchy 组合导数非线性薛定谔孤子层次结构
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00040-5
Wen-Xiu Ma
{"title":"A combined derivative nonlinear SchrÖdinger soliton hierarchy","authors":"Wen-Xiu Ma","doi":"10.1016/S0034-4877(24)00040-5","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00040-5","url":null,"abstract":"<div><p>This paper aims to study a Kaup-Newell type matrix eigenvalue problem with four potentials, based on a specific matrix Lie algebra, and construct an associated soliton hierarchy of combined derivative nonlinear Schrödinger (NLS) equations, within the zero curvature formulation. The Liouville integrability of the resulting soliton hierarchy is shown by exploring its hereditary recursion operator and bi-Hamiltonian formulation. The first nonlinear example provides an integrable model consisting of combined derivative NLS equations with two arbitrary constants.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constructive Gibbs measures for the Ising model on the Cayley tree Cayley 树上伊辛模型的构造吉布斯度量
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00043-0
Muzaffar M. Rahmatullaev, Zulxumor A. Burxonova
{"title":"Constructive Gibbs measures for the Ising model on the Cayley tree","authors":"Muzaffar M. Rahmatullaev,&nbsp;Zulxumor A. Burxonova","doi":"10.1016/S0034-4877(24)00043-0","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00043-0","url":null,"abstract":"<div><p>In the present paper, we construct new Gibbs measures for the Ising model on the Cayley tree of order two. Moreover, we find the free energy corresponding to the found measures and compare it with the known ones.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141479223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","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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