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Inverse scattering method via the Gel’fand–Levitan–Marchenko equation for some negative-order nonlinear wave equations 用Gel’fand - levitan - marchenko方程求解负阶非线性波动方程的逆散射方法
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 Biswas-Milovic方程的广义统一方法与某些精确解方法及一般解的比较分析
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 简化(q) -KP和简化(q) -mKP层次之间的规范转换
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
Einstein–dilaton-four–Maxwell holographic anisotropic models 爱因斯坦膨胀- 4 -麦克斯韦全息各向异性模型
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010118
I. Ya. Aref’eva, K. A. Rannu, P. S. Slepov
{"title":"Einstein–dilaton-four–Maxwell holographic anisotropic models","authors":"I. Ya. Aref’eva,&nbsp;K. A. Rannu,&nbsp;P. S. Slepov","doi":"10.1134/S0040577925010118","DOIUrl":"10.1134/S0040577925010118","url":null,"abstract":"<p> In recent studies on holographic QCD, the consideration of five-dimensional Einstein–dilaton–Maxwell models has played a crucial role. Typically, one Maxwell field is associated with the chemical potential, while additional Maxwell fields are used to describe the anisotropy of the model. A more general scenario involves up to four Maxwell fields. The second field represents spatial longitudinal–transverse anisotropy, while the third and fourth fields describe anisotropy induced by an external magnetic field. We consider an ansatz for the metric characterized by four functions at zero temperature and five functions at nonzero temperature. The Maxwell field related to the chemical potential is treated with the electric ansatz, as is customary, whereas the remaining three Maxwell fields are treated with a magnetic ansatz. We demonstrate that in the fully anisotropic diagonal case, only six out of the seven equations are independent. One of the matter equations (either the dilaton or the vector potential equation) follows from the Einstein equations and the remaining matter equation. This redundancy arises due to the Bianchi identity for the Einstein tensor and the specific form of the energy–momentum tensor in the model. A procedure for solving this system of six equations is provided. This method generalizes previously studied cases involving up to three Maxwell fields. In the solution with three magnetic fields case, our analysis shows that the dilaton equation is a consequence of the five Einstein equations and the equation for the vector potential. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"140 - 153"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109771","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
Exact smooth and nonsmooth solutions for integro-partial differential equations by rapidly convergent approximation method 用快速收敛逼近法求积分-偏微分方程的光滑和非光滑精确解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010052
P. K. Das
{"title":"Exact smooth and nonsmooth solutions for integro-partial differential equations by rapidly convergent approximation method","authors":"P. K. Das","doi":"10.1134/S0040577925010052","DOIUrl":"10.1134/S0040577925010052","url":null,"abstract":"<p> We investigate a general class of second-order integro–ordinary-differential equations with arbitrary-power nonlinear terms, which can be used as a mathematical model for a variety of important physical areas in mathematics, mathematical physics, and applied sciences. The exact smooth and nonsmooth solutions of the aforementioned integro–differential equation in terms of the Gauss hypergeometric function are obtained here for the first time using the rapidly convergent approximation method. The prerequisites for the existence of such solutions are outlined in a theorem. Additionally, a few theorems are presented that contain the conditions under which our derived nonsmooth solution can be viewed as a weak solution. Using the aforementioned results, we obtain exact smooth and nonsmooth solutions of the following nonlinear integro-partial differential equations: the <span>((1+1))</span>-dimensional integro–differential Ito equation, the <span>((3+1))</span>-dimensional Yu–Toda–Sasa–Fukuyama equation, and the Calogero–Bogoyavlenskii–Schiff equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"53 - 68"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109777","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
Long-time asymptotic behavior and bound state soliton solutions for a generalized derivative nonlinear Schrödinger equation 广义导数非线性Schrödinger方程的长时间渐近行为和束缚态孤子解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-01-27 DOI: 10.1134/S0040577925010076
Bingshui Wang, Qiulan Zhao, Xinyue Li
{"title":"Long-time asymptotic behavior and bound state soliton solutions for a generalized derivative nonlinear Schrödinger equation","authors":"Bingshui Wang,&nbsp;Qiulan Zhao,&nbsp;Xinyue Li","doi":"10.1134/S0040577925010076","DOIUrl":"10.1134/S0040577925010076","url":null,"abstract":"<p> We obtain the long-time asymptotic behavior and <span>(N)</span>th-order bound state soliton solutions of a generalized derivative nonlinear Schrödinger (g-DNLS) equation via the Riemann–Hilbert method. First, in the process of direct scattering, the spectral analysis of the Lax pair is performed, from which a Riemann–Hilbert problem (RHP) is established for the g-DNLS equation. Next, in the process of inverse scattering, different from traditional solution finding schemes, we give some Laurent expansions of related functions and use them to obtain solutions of the RHP for the reflection coefficients under different conditions, such as a single pole and multiple poles, where we obtain new <span>(N)</span>th-order bound state soliton solutions. Based on the originally constructed RHP, we use the <span>(overline{partial})</span>-steepest descent method to explicitly find long-time asymptotic behavior of the solutions of the g-DNLS equation. With this method, we obtain an accuracy of the asymptotic behavior of the solution that is currently not obtainable by the direct method of partial differential equations. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 1","pages":"85 - 105"},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109776","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
Beta-function dependence on the running coupling in holographic QCD models 全息QCD模型中运行耦合的β函数依赖
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120080
I. Ya. Aref’eva, A. Hajilou, P. S. Slepov, M. K. Usova
{"title":"Beta-function dependence on the running coupling in holographic QCD models","authors":"I. Ya. Aref’eva,&nbsp;A. Hajilou,&nbsp;P. S. Slepov,&nbsp;M. K. Usova","doi":"10.1134/S0040577924120080","DOIUrl":"10.1134/S0040577924120080","url":null,"abstract":"<p> We study the dependence of the beta-function on the running coupling constant in holographic models supported by the Einstein–dilaton–Maxwell action for light and heavy quarks. The dilaton defines the running coupling of the models. Its dependence on boundary conditions leads to the running coupling dependence on them. However, the behavior of the <span>(beta)</span>-function as a function of the running coupling does not depend significantly on the boundary condition. The corresponding <span>(beta)</span>-functions are negative and monotonically decreasing functions, and have jumps at first-order phase transitions for both light and heavy quarks. In addition, we compare our holographic results for the <span>(beta)</span>-function as a function of the running coupling with perturbative results obtained within <span>(2)</span>-loop calculations. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2132 - 2143"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889881","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
Maurer–Cartan methods in perturbative quantum mechanics 微扰量子力学中的毛雷尔-卡坦方法
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120109
A. S. Losev, T. V. Sulimov
{"title":"Maurer–Cartan methods in perturbative quantum mechanics","authors":"A. S. Losev,&nbsp;T. V. Sulimov","doi":"10.1134/S0040577924120109","DOIUrl":"10.1134/S0040577924120109","url":null,"abstract":"<p> We reformulate the time-independent Schrödinger equation as a Maurer–Cartan equation on the superspace of eigensystems of the former equation. We then twist the differential such that its cohomology becomes the space of solutions with a fixed energy. A perturbation of the Hamiltonian corresponds to a deformation of the twisted differential, leading to a simple recursive relation for the eigenvalue and eigenfunction corrections. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2155 - 2164"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890489","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
Darboux transformations for the discrete versions of the KP and strict KP hierarchies 离散KP和严格KP层次的达布变换
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120031
G. F. Helminck, V. A. Poberezhny, S. V. Polenkova
{"title":"Darboux transformations for the discrete versions of the KP and strict KP hierarchies","authors":"G. F. Helminck,&nbsp;V. A. Poberezhny,&nbsp;S. V. Polenkova","doi":"10.1134/S0040577924120031","DOIUrl":"10.1134/S0040577924120031","url":null,"abstract":"<p> We introduce the notion of Darboux transformations for the discrete KP hierarchy and its strict version, and present an explicit form of these transformations for the solutions of discrete KP and discrete strict KP hierarchies constructed in our previous work. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2031 - 2048"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889918","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 extended 2-dimensional Toda lattice models 关于扩展的二维Toda晶格模型
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120043
Conghan Wang, Shangshuai Li, Da-jun Zhang
{"title":"On the extended 2-dimensional Toda lattice models","authors":"Conghan Wang,&nbsp;Shangshuai Li,&nbsp;Da-jun Zhang","doi":"10.1134/S0040577924120043","DOIUrl":"10.1134/S0040577924120043","url":null,"abstract":"<p> An extended <span>(2)</span>-dimensional Toda lattice equation is investigated by means of the Cauchy matrix approach. We introduce a direction parameter in the extension and represented the equation as a coupled system in a <span>(3)</span>-dimensional space. The equation can also be considered as a negative-order member in one direction of the discrete Kadomtsev–Petviashvili equation. By introducing the <span>(tau)</span>-function and an auxiliary direction, the equation can be bilinearized in a <span>(4)</span>-dimensional space with a single <span>(tau)</span>-function. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2049 - 2061"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889917","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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