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Rational solutions of nonautonomous quadrilateral equations by the bilinearization of Bäcklund transformation systems Bäcklund变换系统双线性化非自治四边形方程的有理解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040051
Danda Zhang, Liya Zhu, Yingying Sun
{"title":"Rational solutions of nonautonomous quadrilateral equations by the bilinearization of Bäcklund transformation systems","authors":"Danda Zhang,&nbsp;Liya Zhu,&nbsp;Yingying Sun","doi":"10.1134/S0040577925040051","DOIUrl":"10.1134/S0040577925040051","url":null,"abstract":"<p> Rational solutions of several nonautonomous quadrilateral equations in the ABS and ABS* list are obtained in a neat form of Casoratians, which mostly relies on a single <span>(tau)</span> function. The corresponding nonautonomous bilinear equations are listed in difference and differential–difference forms by introducing an auxiliary variable. Instead of bilinearizing quadrilateral equations, we present their related Bäcklund transformation systems, which directly reduce to bilinear equations by specific transformations. As an application, a result related to the discrete Painlevé equation is given. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"576 - 596"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875267","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
Integration of the generalized Camassa–Holm equation in the class of periodic functions 周期函数类中广义Camassa-Holm方程的积分
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040075
B. A. Babajanov, D. O. Atajonov
{"title":"Integration of the generalized Camassa–Holm equation in the class of periodic functions","authors":"B. A. Babajanov,&nbsp;D. O. Atajonov","doi":"10.1134/S0040577925040075","DOIUrl":"10.1134/S0040577925040075","url":null,"abstract":"<p> We study periodic solutions of the generalized Camassa–Holm equation (CH-<span>(gamma)</span> equation). We show that the generalized CH-<span>(gamma)</span> equation is also an important theoretical model because it is a completely integrable system. We obtain representation for periodic solutions of the generalized CH-<span>(gamma)</span> equation in the framework of the inverse spectral problem for a weighted Sturm–Liouville operator. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"624 - 635"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875424","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
Equivalence of two constructions for (widehat{sl}_2)-integrable hierarchies (widehat{sl}_2) -可积层次结构的两个结构的等价性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040063
Panpan Dang, Yajuan Li, Yuanyuan Zhang, Jipeng Cheng
{"title":"Equivalence of two constructions for (widehat{sl}_2)-integrable hierarchies","authors":"Panpan Dang,&nbsp;Yajuan Li,&nbsp;Yuanyuan Zhang,&nbsp;Jipeng Cheng","doi":"10.1134/S0040577925040063","DOIUrl":"10.1134/S0040577925040063","url":null,"abstract":"<p> We discuss the equivalence between the Date–Jimbo–Kashiwara–Miwa (DJKM) construction and the Kac–Wakimoto (KW) construction of <span>(widehat{sl}_2)</span>-integrable hierarchies within the framework of bilinear equations. The DJKM method has achieved remarkable success in constructing integrable hierarchies associated with classical A, B, C, D affine Lie algebras. In contrast, the KW method exhibits broader applicability, as it can be employed even for exceptional E, F, G affine Lie algebras. However, a significant drawback of the KW construction lies in the great difficulty of obtaining Lax equations for the corresponding integrable hierarchies. Conversely, in the DJKM construction, Lax structures for numerous integrable hierarchies can be derived. The derivation of Lax equations from bilinear equations in the KW construction remains an open problem. Consequently, demonstrating the equivalent DJKM construction for the integrable hierarchies obtained via the KW construction would be highly beneficial for obtaining the corresponding Lax structures. In this paper, we use the language of lattice vertex algebras to establish the equivalence between the DJKM and KW methods in the <span>(widehat{sl}_2)</span>-integrable hierarchy for principal and homogeneous representations. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"597 - 623"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875283","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
Linear representations of the Lie algebra of the diffeomorphism group in (mathbb{R}^d) 中的微分同构群李代数的线性表示 (mathbb{R}^d)
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040014
M. I. Gozman
{"title":"Linear representations of the Lie algebra of the diffeomorphism group in (mathbb{R}^d)","authors":"M. I. Gozman","doi":"10.1134/S0040577925040014","DOIUrl":"10.1134/S0040577925040014","url":null,"abstract":"<p> A family of representations of the Lie algebra of the diffeomorphism group in <span>(mathbb{R}^d)</span> is studied. A method for constructing representations of this family is proposed. Equations for matrices describing the action of the Lie algebra on the representation space are obtained. It is shown that the developed formalism is suitable for describing representations under which fields of linear homogeneous geometric objects are transformed. The formalism is shown to allow describing representations for which the representation space vectors cannot be expressed in terms of fields of linear homogeneous geometric objects. An example of such a representation is studied. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"525 - 547"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875286","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
Asymptotic solution convergence to a traveling wave in the Kolmogorov–Petrovskii–Piskunov equation Kolmogorov-Petrovskii-Piskunov方程行波渐近解的收敛性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040038
L. A. Kalyakin
{"title":"Asymptotic solution convergence to a traveling wave in the Kolmogorov–Petrovskii–Piskunov equation","authors":"L. A. Kalyakin","doi":"10.1134/S0040577925040038","DOIUrl":"10.1134/S0040577925040038","url":null,"abstract":"<p> For a semilinear parabolic partial differential equation, we consider an asymptotic solution that converges to a traveling wave at large times <span>(t)</span>. The velocity of such a wave is time dependent, and we construct the asymptotics as <span>(ttoinfty)</span>. We find that the asymptotics contains logarithms and cannot be constructed in the form of a power series. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"556 - 571"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875285","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
Explicit Bargmann-type isomorphism between Berezin and Smolyanov representations of bosonic Fock spaces 玻色子Fock空间的Berezin和Smolyanov表示之间的显式bargmann型同构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040105
N. N. Shamarov, M. V. Shamolin
{"title":"Explicit Bargmann-type isomorphism between Berezin and Smolyanov representations of bosonic Fock spaces","authors":"N. N. Shamarov,&nbsp;M. V. Shamolin","doi":"10.1134/S0040577925040105","DOIUrl":"10.1134/S0040577925040105","url":null,"abstract":"<p> We construct a Bargmann-type isomorphism defined by the one-particle part <span>(H)</span> of the Fock space <span>(Gamma(H))</span> for an infinite-dimensional space <span>(H)</span> with involution. The formulas obtained also make sense in the case <span>(dim H&lt;infty)</span> and are closely related to the Segal–Bargmann space. Central to the construction is the notion of a shift-invariant distribution in the case of an infinite-dimensional domain of test functions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"665 - 670"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875423","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
Feynman integral in QFT and white noise on a compactified version of space–time with a Lie group structure 具有李群结构的紧化时空上的QFT和白噪声中的费曼积分
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040117
J. Wawrzycki
{"title":"Feynman integral in QFT and white noise on a compactified version of space–time with a Lie group structure","authors":"J. Wawrzycki","doi":"10.1134/S0040577925040117","DOIUrl":"10.1134/S0040577925040117","url":null,"abstract":"<p> We present a rigorous construction of the Feynman integral on the compactified Einstein Universe using white noise calculus. Our construction of functional averaging can also be thought of as a solution to a problem posed by Bogoliubov and Shirkov. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"671 - 689"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875421","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
On the Rayleigh–Schrödinger coefficients for the eigenvalues of regular perturbations of an anharmonic oscillator 非谐振子正则扰动特征值的Rayleigh-Schrödinger系数
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040099
Kh. K. Ishkin
{"title":"On the Rayleigh–Schrödinger coefficients for the eigenvalues of regular perturbations of an anharmonic oscillator","authors":"Kh. K. Ishkin","doi":"10.1134/S0040577925040099","DOIUrl":"10.1134/S0040577925040099","url":null,"abstract":"<p> We identify a class of perturbations of a complex anharmonic oscillator <span>(H)</span> for which the known formulas for the Rayleigh–Schrödinger coefficients can be significantly simplified. We investigate the effect of the spectral instability of the operator <span>(H)</span> on the behavior of the sequence of first perturbative corrections. We show that if <span>(H)</span> is not self-adjoint and the perturbation is finite and has finite smoothness at the right end of its support, then this sequence exponentially increases at infinity. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"650 - 664"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875422","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
On alleged solutions of the cubically nonlinear Schrödinger equation 关于三次非线性Schrödinger方程的所谓解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S004057792504004X
H. W. Schürmann, V. S. Serov
{"title":"On alleged solutions of the cubically nonlinear Schrödinger equation","authors":"H. W. Schürmann,&nbsp;V. S. Serov","doi":"10.1134/S004057792504004X","DOIUrl":"10.1134/S004057792504004X","url":null,"abstract":"<p> On the basis of analytic results, we present a numerical example that indicates the inconsistency of a widely used ansatz for the cubically nonlinear Schrödinger equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"572 - 575"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875284","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
(Omega)-Spectrum in topological phases (Omega)-拓扑相的谱
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040026
E. A. Teplyakov
{"title":"(Omega)-Spectrum in topological phases","authors":"E. A. Teplyakov","doi":"10.1134/S0040577925040026","DOIUrl":"10.1134/S0040577925040026","url":null,"abstract":"<p> Symmetry-protected topological phases are an active field of research in condensed matter physics. The classification of symmetry-protected topological phases is an important problem in mathematics and theoretical physics. In this paper, a direct approach based on the use of methods of homotopy theory and the theory of infinite loop spaces is proposed to describe the <span>(Omega)</span>-spectra and the generalized cohomology theories arising in the classification of topological phases. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"548 - 555"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875290","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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