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Nonlocal symmetries of the Degasperis–Procesi equation
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010088
Xiaoyong Li, Changzheng Qu
{"title":"Nonlocal symmetries of the Degasperis–Procesi equation","authors":"Xiaoyong Li,&nbsp;Changzheng Qu","doi":"10.1134/S0040577925010088","DOIUrl":"10.1134/S0040577925010088","url":null,"abstract":"<p> We study nonlocal symmetries of the Degasperis–Procesi equation, which are shown to be closely related to its integrable structure. First, applying the Hamiltonian operator to the gradients of the spectral parameter, we construct nonlocal symmetries of the Kaup–Kupershmidt equation. Next, we show that the nonlocal symmetries can be prolonged to local symmetries for a prolonged system by introducing new dependent variables. Finally, applying the Liouville transformation relating the Degasperis–Procesi and Kaup–Kupershmidt hierarchies, we obtain the corresponding nonlocal symmetries of the Degasperis–Procesi equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"106 - 118"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109774","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
Classification of semidiscrete equations of hyperbolic type. The case of fifth-order symmetries
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010027
R. N. Garifullin
{"title":"Classification of semidiscrete equations of hyperbolic type. The case of fifth-order symmetries","authors":"R. N. Garifullin","doi":"10.1134/S0040577925010027","DOIUrl":"10.1134/S0040577925010027","url":null,"abstract":"<p> We classify the semidiscrete hyperbolic-type equations. We study the class of equations of the form </p><p> where the unknown function <span>(u_n(x))</span> depends on one discrete variable <span>(n)</span> and one continuous variable <span>(x)</span>. The classification is based on the requirement of the existence of higher symmetries. We consider the case where the symmetry has the fifth order in the continuous direction. As a result, we obtain a list of four equations with the required conditions, for each of which the higher symmetry in the discrete direction is written. For one of the obtained equations, we construct a Lax representation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"10 - 19"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109761","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
Algebro-geometric quasiperiodic solutions of the nonlocal reverse space–time sine-Gordon equation
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010064
Liang Guan, Xianguo Geng, Xue Geng
{"title":"Algebro-geometric quasiperiodic solutions of the nonlocal reverse space–time sine-Gordon equation","authors":"Liang Guan,&nbsp;Xianguo Geng,&nbsp;Xue Geng","doi":"10.1134/S0040577925010064","DOIUrl":"10.1134/S0040577925010064","url":null,"abstract":"<p> Based on the theory of hyperelliptic curves, the algebraic curve method is extended to construct algebro-geometric quasiperiodic solutions of nonlocal reverse space–time soliton equations. The nonlocal reverse space–time sine-Gordon equation is chosen as an example to illustrate our method. Given the Lax matrix of the nonlocal reverse space–time sine-Gordon equation, we introduce an algebraic hyperelliptic curve <span>(mathcal K_n)</span> of genus <span>(n)</span>, from which the Dubrovin-type equations, a meromorphic function <span>(phi)</span>, and a Baker–Akhiezer function <span>(psi_{1})</span> are found. Using the theory of algebraic curves, the nonlocal reverse space–time sine-Gordon flows are straightened by using the Abel–Jacobi coordinates. In accordance with the asymptotic properties of the Baker–Akhiezer function, we construct explicit theta-function representations of the Baker–Akhiezer function and the meromorphic function, including that for solutions of the nonlocal reverse space–time sine-Gordon equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"69 - 84"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109775","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
Finite entangling regions and information paradox in charged black holes
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S004057792501012X
A. I. Belokon
{"title":"Finite entangling regions and information paradox in charged black holes","authors":"A. I. Belokon","doi":"10.1134/S004057792501012X","DOIUrl":"10.1134/S004057792501012X","url":null,"abstract":"<p> We study the influence of the electric charge of a Reissner–Nordström black hole on the dynamics of the fine-grained entropy of Hawking radiation collected in finite entangling regions. We demonstrate that for certain sizes of finite regions, it is always possible to choose a value of the charge such that no information paradox formulated for finite entangling regions arises. For completeness, we explore how entanglement islands influence the described picture. We find that at small values of the electric charge, there is a discontinuity in the entropy due to the disappearance of the island, and as the charge increases, the island ceases to ever dominate throughout entire evolution. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"154 - 169"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109672","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
Fermionic fields in a four-dimensional (Lambda) Bonnor–Melvin space–time
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010131
F. Ahmed, N. Candemir, A. Bouzenada
{"title":"Fermionic fields in a four-dimensional (Lambda) Bonnor–Melvin space–time","authors":"F. Ahmed,&nbsp;N. Candemir,&nbsp;A. Bouzenada","doi":"10.1134/S0040577925010131","DOIUrl":"10.1134/S0040577925010131","url":null,"abstract":"<p> We investigate how the gravitational field generated by a four-dimensional electrovacuum cosmological space–time influences the dynamics of fermionic fields governed by the Dirac equation, while also considering the effects of topology. We derive the radial wave equation corresponding to the relativistic Dirac equation and obtain analytical solutions for the energy levels and wave functions of the fermionic field within our framework. Our analysis reveals that various parameters, including the cosmological constant, the parameter responsible for space topology, and quantum numbers, play significant roles in determining the eigenvalues of the quantum particles. Specifically, we demonstrate that the presence of the topological parameter disrupts the degeneracy of the energy spectrum. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"170 - 182"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109673","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
Rogue waves of the ((2+1))-dimensional integrable reverse space–time nonlocal Schrödinger equation
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010040
Yindi Liu, Zhonglong Zhao
{"title":"Rogue waves of the ((2+1))-dimensional integrable reverse space–time nonlocal Schrödinger equation","authors":"Yindi Liu,&nbsp;Zhonglong Zhao","doi":"10.1134/S0040577925010040","DOIUrl":"10.1134/S0040577925010040","url":null,"abstract":"<p> The <span>((2+1))</span>-dimensional integrable reverse space–time nonlocal Schrödinger equation is investigated. It has many applications in fluid mechanics, quantum mechanics and plasma physics. The one-periodic wave solution and two kinds of two-periodic wave solutions are obtained via the bilinear method. Taking a long-wave limit of the periodic wave solutions generates two types of rogue waves, which are called kink-shaped and W-shaped line rogue waves. We also employ the asymptotic analysis to interpret the dynamical properties of the kink-shaped rogue wave. The higher-order rogue waves are generated by the interaction of the above two types of rogue waves. Their plots exhibit interesting patterns with several different outlines. Furthermore, the semirational solutions are obtained, which arise from the interactions between rogue waves and the periodic line wave. They can be divided into two types: those that interact and return to the periodic wave background and those that interact and return to the constant background. We extend our analysis method to analyze more complex solutions for multidimensional nonlocal integrable systems. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"34 - 52"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109759","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 integrability of nonlinear wave equations and the semiclassical limit of Lax pairs
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010015
A. M. Kamchatnov
{"title":"Asymptotic integrability of nonlinear wave equations and the semiclassical limit of Lax pairs","authors":"A. M. Kamchatnov","doi":"10.1134/S0040577925010015","DOIUrl":"10.1134/S0040577925010015","url":null,"abstract":"<p> We introduce the concept of asymptotic integrability of nonlinear wave equations, which means the integrability of Hamilton equations describing the propagation of a high-frequency wave packet along a smooth profile whose dynamics obeys the dispersionless limit of the original equations. We show that this limit case of complete integrability allows expressing the semiclassical limit of Lax pairs in terms of the dispersion law for linear waves and an integral of the Hamilton equations for the packet. If the Lax pair does not depend on derivatives of the wave variables, then the semiclassical limit coincides with the exact expressions. We illustrate the theory with specific examples. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"1 - 9"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109762","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
Inverse scattering method via the Gel’fand–Levitan–Marchenko equation for some negative-order nonlinear wave equations
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010039
M. I. Ismailov, C. Sabaz
{"title":"Inverse scattering method via the Gel’fand–Levitan–Marchenko equation for some negative-order nonlinear wave equations","authors":"M. I. Ismailov,&nbsp;C. Sabaz","doi":"10.1134/S0040577925010039","DOIUrl":"10.1134/S0040577925010039","url":null,"abstract":"<p> A class of negative-order Ablowitz–Kaup–Newell–Segur nonlinear evolution equations are obtained by applying the Lax hierarchy of a first-order linear system of three equations. The inverse scattering problem on the line is examined in the cases where the linear system becomes the classical Zakharov–Shabat system with real antisymmetric and real symmetric potentials. Referring to these results, the <span>(N)</span>-soliton solutions for the integro-differential version of the nonlinear Klein–Gordon equation coupled to a scalar field and the negative-order modified Korteweg-de Vries equation are obtained by using the inverse scattering method via the Gel’fand–Levitan–Marchenko equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"20 - 33"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109760","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
Comparative analysis of the generalized unified method with some exact solution methods and general solutions of the Biswas–Milovic equation
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S004057792501009X
T. Aydemir
{"title":"Comparative analysis of the generalized unified method with some exact solution methods and general solutions of the Biswas–Milovic equation","authors":"T. Aydemir","doi":"10.1134/S004057792501009X","DOIUrl":"10.1134/S004057792501009X","url":null,"abstract":"<p> The aim of this study is twofold. First, we compare the generalized unified method (GUM), which is a new expansion method to solve nonlinear partial differential equations (NPDEs), with some methods frequently used for finding exact solutions of NPDEs. We conclude that the GUM gives more general solutions efficiently, in compact form, and with free parameters. Moreover, the algorithm of the GUM is straightforward and easy to implement on a computer. Second, as a practical example and a demonstration of effectiveness, we apply the GUM to the Biswas–Milovic equation (BME). The BME is derived from a generalized nonlinear Schrödinger equation. The BME appears in many applied fields such as the propagation of waves in nonlinear optics. We consider Kerr, power, parabolic, and dual-power-law nonlinearities of the BME. Using the GUM, we obtain the exact solution of the BME in an elegant way. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"119 - 130"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109773","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
Gauge transformations between reduced (q)-KP and reduced (q)-mKP hierarchies
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010106
Shilong Huang, Chuanzhong Li
{"title":"Gauge transformations between reduced (q)-KP and reduced (q)-mKP hierarchies","authors":"Shilong Huang,&nbsp;Chuanzhong Li","doi":"10.1134/S0040577925010106","DOIUrl":"10.1134/S0040577925010106","url":null,"abstract":"<p> We reduce the <span>(q)</span>-KP hierarchy and the <span>(q)</span>-mKP hierarchy. By using the link between the <span>(q)</span>-KP hierarchy and the <span>(q)</span>-mKP hierarchy, we obtain a relation between the <span>(q)</span>-KdV and the <span>(q)</span>-mKdV hierarchies, as well as a relation between the <span>(q)</span>-Boussinesq and <span>(q)</span>-mBoussinesq equations. The connection between them can also be established by a gauge transformation. We verify that when in the limit <span>(qto 1)</span>, these relations correspond to the results for classical systems. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"131 - 139"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109772","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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