Pub Date : 2024-06-25DOI: 10.1134/s0040577924060011
M. A. Bezuglov, A. I. Onishchenko
Abstract
Hypergeometric functions of one and many variables play an important role in various branches of modern physics and mathematics. We often encounter hypergeometric functions with indices linearly dependent on a small parameter with respect to which we need to perform Laurent expansions. Moreover, it is desirable that such expansions be expressed in terms of well-known functions that can be evaluated with arbitrary precision. To solve this problem, we use the method of differential equations and the reduction of corresponding differential systems to a canonical basis. In this paper, we are interested in the generalized hypergeometric functions of one variable and in the Appell and Lauricella functions and their expansions in terms of the Goncharov polylogarithms. Particular attention is paid to the case of rational indices of the considered hypergeometric functions when the reduction to the canonical basis involves a nontrivial variable change. The paper comes with a Mathematica package Diogenes, which provides an algorithmic implementation of the required steps.
{"title":"Expansion of hypergeometric functions in terms of polylogarithms with a nontrivial change of variables","authors":"M. A. Bezuglov, A. I. Onishchenko","doi":"10.1134/s0040577924060011","DOIUrl":"https://doi.org/10.1134/s0040577924060011","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Hypergeometric functions of one and many variables play an important role in various branches of modern physics and mathematics. We often encounter hypergeometric functions with indices linearly dependent on a small parameter with respect to which we need to perform Laurent expansions. Moreover, it is desirable that such expansions be expressed in terms of well-known functions that can be evaluated with arbitrary precision. To solve this problem, we use the method of differential equations and the reduction of corresponding differential systems to a canonical basis. In this paper, we are interested in the generalized hypergeometric functions of one variable and in the Appell and Lauricella functions and their expansions in terms of the Goncharov polylogarithms. Particular attention is paid to the case of rational indices of the considered hypergeometric functions when the reduction to the canonical basis involves a nontrivial variable change. The paper comes with a Mathematica package <span>Diogenes</span>, which provides an algorithmic implementation of the required steps. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503131","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}
Pub Date : 2024-06-25DOI: 10.1134/s0040577924060060
Hui Mao
Abstract
Multibreather-like solutions in determinant form for the real and complex reverse space–time nonlocal defocusing short-pulse equations are constructed via Darboux transformations and nonlocal reductions. It is shown that the multibreather-like solutions of these two equations can be obtained only by reducing the even multisoliton solutions of the two-component short-pulse equation. As examples, (1,2)-breather-like solutions and their dynamics are illustrated graphically.
{"title":"Multibreather-like solutions of the real and complex reverse space–time nonlocal defocusing short-pulse equations","authors":"Hui Mao","doi":"10.1134/s0040577924060060","DOIUrl":"https://doi.org/10.1134/s0040577924060060","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Multibreather-like solutions in determinant form for the real and complex reverse space–time nonlocal defocusing short-pulse equations are constructed via Darboux transformations and nonlocal reductions. It is shown that the multibreather-like solutions of these two equations can be obtained only by reducing the even multisoliton solutions of the two-component short-pulse equation. As examples, <span>(1,2)</span>-breather-like solutions and their dynamics are illustrated graphically. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514122","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}
Pub Date : 2024-06-25DOI: 10.1134/s0040577924060096
K. R. Atalikov, A. V. Zotov
Abstract
We consider the classical integrable ((1+1)) trigonometric (gl_N) Landau–Lifshitz models constructed by means of quantum (R)-matrices that also satisfy the associative Yang–Baxter equation. It is shown that a ((1+1)) field analogue of the trigonometric Calogero–Moser–Sutherland model is gauge equivalent to the Landau–Lifshitz model that arises from the Antonov–Hasegawa–Zabrodin trigonometric nonstandard (R)-matrix. The latter generalizes Cherednik’s (7)-vertex (R)-matrix in the (GL_2) case to the case of (GL_N). An explicit change of variables between the ((1+1)) models is obtained.
{"title":"Gauge equivalence of $$1+1$$ Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model","authors":"K. R. Atalikov, A. V. Zotov","doi":"10.1134/s0040577924060096","DOIUrl":"https://doi.org/10.1134/s0040577924060096","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the classical integrable <span>((1+1))</span> trigonometric <span>(gl_N)</span> Landau–Lifshitz models constructed by means of quantum <span>(R)</span>-matrices that also satisfy the associative Yang–Baxter equation. It is shown that a <span>((1+1))</span> field analogue of the trigonometric Calogero–Moser–Sutherland model is gauge equivalent to the Landau–Lifshitz model that arises from the Antonov–Hasegawa–Zabrodin trigonometric nonstandard <span>(R)</span>-matrix. The latter generalizes Cherednik’s <span>(7)</span>-vertex <span>(R)</span>-matrix in the <span>(GL_2)</span> case to the case of <span>(GL_N)</span>. An explicit change of variables between the <span>((1+1))</span> models is obtained. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514125","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}
Pub Date : 2024-06-25DOI: 10.1134/s0040577924060102
M. Hasegawa
Abstract
The effects of external magnetic fields on monopoles, spectra of the overlap Dirac operator, instantons, and the mass of the eta-prime meson are examined by conducting lattice QCD simulations. The uniform external magnetic field is applied to gauge field configurations with (N_f=2+1) flavor quarks. The bare quark masses are tuned in order to obtain the physical values of the pion mass and of the (m_s/m_{u,d}) ratio. Standard configurations and configurations with an applied external magnetic field are generated in the color confinement and deconfinement phases. The intensity of the external magnetic field varies from (e|B|=0.57,mathrm{GeV}^2) to (e|B|=1.14,mathrm{GeV}^2). To examine the influence of the external magnetic field on monopoles, we first calculate the monopole density, measure the lengths of the monopole loops, and compare them with the absolute value of the Polyakov loops. Next, using the generated configurations, we compute the eigenvalues and eigenvectors of the overlap Dirac operator, which preserves exact chiral symmetry. To investigate how external magnetic fields affect the spectra of the overlap Dirac operator, we compute spectral densities, compare fluctuations of the eigenvalues of the overlap Dirac operator with the predictions of random matrix theory, and estimate the number of instantons and anti-instantons from the topological charges. In addition, we analyze smearing effects on these observables and chiral symmetry breaking. Finally, we calculate the decay constant of the pseudoscalar meson, the chiral condensate, and the square mass of the eta-prime meson using the eigenvalues and eigenvectors. We then extrapolate the numerical results in the chiral limit and demonstrate the effects of external magnetic fields on the extrapolation results. This article presents preliminary results.
{"title":"Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields","authors":"M. Hasegawa","doi":"10.1134/s0040577924060102","DOIUrl":"https://doi.org/10.1134/s0040577924060102","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The effects of external magnetic fields on monopoles, spectra of the overlap Dirac operator, instantons, and the mass of the eta-prime meson are examined by conducting lattice QCD simulations. The uniform external magnetic field is applied to gauge field configurations with <span>(N_f=2+1)</span> flavor quarks. The bare quark masses are tuned in order to obtain the physical values of the pion mass and of the <span>(m_s/m_{u,d})</span> ratio. Standard configurations and configurations with an applied external magnetic field are generated in the color confinement and deconfinement phases. The intensity of the external magnetic field varies from <span>(e|B|=0.57,mathrm{GeV}^2)</span> to <span>(e|B|=1.14,mathrm{GeV}^2)</span>. To examine the influence of the external magnetic field on monopoles, we first calculate the monopole density, measure the lengths of the monopole loops, and compare them with the absolute value of the Polyakov loops. Next, using the generated configurations, we compute the eigenvalues and eigenvectors of the overlap Dirac operator, which preserves exact chiral symmetry. To investigate how external magnetic fields affect the spectra of the overlap Dirac operator, we compute spectral densities, compare fluctuations of the eigenvalues of the overlap Dirac operator with the predictions of random matrix theory, and estimate the number of instantons and anti-instantons from the topological charges. In addition, we analyze smearing effects on these observables and chiral symmetry breaking. Finally, we calculate the decay constant of the pseudoscalar meson, the chiral condensate, and the square mass of the eta-prime meson using the eigenvalues and eigenvectors. We then extrapolate the numerical results in the chiral limit and demonstrate the effects of external magnetic fields on the extrapolation results. This article presents preliminary results. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514126","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}
Pub Date : 2024-05-24DOI: 10.1134/s0040577924050118
Y. Goutal, F. Serdouk, A. Boumali, M. L. Benkhedir
Abstract
The use of the multiple-trapping (MT) model to comprehend the transport of nonequilibrium charge carriers in amorphous semiconductors has proven highly effective. Under specific conditions, this model generates anomalous diffusion equations characterized by fractional time derivatives. This underscores the utility of the MT model in interpreting fractional transport equations, establishing initial and boundary conditions, and developing numerical methods for solving fractional kinetic equations. Also, this work provides a concise overview of applying fractional MT equations to address challenges in time-of-flight (TOF) experiments. Furthermore, it delves into the connection between the MT model and generalized fractional kinetic equations. In addition, the study introduces analytic approximate solutions of the fractional diffusion equation, incorporating MT phenomena and employing Laplace transforms. This approach is suitable for analyzing both the pre- and post-regimes of TOF transient current, applicable to amorphous semiconductors that display either nondispersive or dispersive transport characteristics. The effectiveness of this method is illustrated through numerical simulations of TOF transient current using the inverse Laplace transform technique with the Padé approximation. The practicality of the method is confronted with the experimental data obtained from thin films of amorphous selenium (a-Se), and the results of this confrontation are deemed satisfactory. The results of this study offer a new promising perspective for the two following reasons. First, employing fractional calculus to address the MT equations introduces a distinct approach compared to methodologies in the existing literature. This is substantiated by the inclusion of memory effects in fractional calculus, implying that the present solution is influenced by preceding time steps. Second, the numerical results demonstrate good agreement with experimental data. Consequently, the introduction of fractional calculus has the potential to offer fresh insights into the behavior of charge carriers in amorphous semiconductors.
{"title":"Fractional multiple trapping model of time-of-flight transient photocurrents in amorphous semiconductors","authors":"Y. Goutal, F. Serdouk, A. Boumali, M. L. Benkhedir","doi":"10.1134/s0040577924050118","DOIUrl":"https://doi.org/10.1134/s0040577924050118","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The use of the multiple-trapping (MT) model to comprehend the transport of nonequilibrium charge carriers in amorphous semiconductors has proven highly effective. Under specific conditions, this model generates anomalous diffusion equations characterized by fractional time derivatives. This underscores the utility of the MT model in interpreting fractional transport equations, establishing initial and boundary conditions, and developing numerical methods for solving fractional kinetic equations. Also, this work provides a concise overview of applying fractional MT equations to address challenges in time-of-flight (TOF) experiments. Furthermore, it delves into the connection between the MT model and generalized fractional kinetic equations. In addition, the study introduces analytic approximate solutions of the fractional diffusion equation, incorporating MT phenomena and employing Laplace transforms. This approach is suitable for analyzing both the pre- and post-regimes of TOF transient current, applicable to amorphous semiconductors that display either nondispersive or dispersive transport characteristics. The effectiveness of this method is illustrated through numerical simulations of TOF transient current using the inverse Laplace transform technique with the Padé approximation. The practicality of the method is confronted with the experimental data obtained from thin films of amorphous selenium (a-Se), and the results of this confrontation are deemed satisfactory. The results of this study offer a new promising perspective for the two following reasons. First, employing fractional calculus to address the MT equations introduces a distinct approach compared to methodologies in the existing literature. This is substantiated by the inclusion of memory effects in fractional calculus, implying that the present solution is influenced by preceding time steps. Second, the numerical results demonstrate good agreement with experimental data. Consequently, the introduction of fractional calculus has the potential to offer fresh insights into the behavior of charge carriers in amorphous semiconductors. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151887","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}
Pub Date : 2024-05-24DOI: 10.1134/s0040577924050015
E. I. Dotsenko
Abstract
The monodromy of the (mathfrak{sl}(2)) Casimir connection is considered. It is shown that the trace of the monodromy operator over an appropriate space of flat sections gives the Jacobi theta constant and incomplete theta functions. A definition of new objects, namely, incomplete Appell–Lerch sums, is given, and their connection with the trace of the monodromy operator is revealed.
Abstract The monodromy of the (mathfrak{sl}(2))卡西米尔连接进行了研究。研究表明，在适当的平面截面空间上的单反转算子的迹给出了雅可比 Theta 常量和不完全 Theta 函数。给出了新对象的定义，即不完全阿贝尔-勒奇和，并揭示了它们与单旋转算子迹的联系。
{"title":"Generalized theta series and monodromy of a Casimir connection. Case of rank 1","authors":"E. I. Dotsenko","doi":"10.1134/s0040577924050015","DOIUrl":"https://doi.org/10.1134/s0040577924050015","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The monodromy of the <span>(mathfrak{sl}(2))</span> Casimir connection is considered. It is shown that the trace of the monodromy operator over an appropriate space of flat sections gives the Jacobi theta constant and incomplete theta functions. A definition of new objects, namely, incomplete Appell–Lerch sums, is given, and their connection with the trace of the monodromy operator is revealed. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149341","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}
Pub Date : 2024-05-24DOI: 10.1134/s004057792405012x
H. Rezki, S. Zaim
Abstract
We use the semiclassical approach to solve the Klein–Gordon and Dirac equations in the presence of a time-varying electric field. Our objective is to calculate the density of particle creation in a cosmological anisotropic Bianchi- I space–time. We demonstrate that when the electric interaction is proportional to the Ricci scalar of curved space–time, the distribution of particles subjected to the electric field transforms into a thermal state.
{"title":"Particle creation in cosmological space–time by a time-varying electric field","authors":"H. Rezki, S. Zaim","doi":"10.1134/s004057792405012x","DOIUrl":"https://doi.org/10.1134/s004057792405012x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We use the semiclassical approach to solve the Klein–Gordon and Dirac equations in the presence of a time-varying electric field. Our objective is to calculate the density of particle creation in a cosmological anisotropic Bianchi- I space–time. We demonstrate that when the electric interaction is proportional to the Ricci scalar of curved space–time, the distribution of particles subjected to the electric field transforms into a thermal state. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152009","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}
Pub Date : 2024-05-24DOI: 10.1134/s0040577924050088
Yu. G. Ignat’ev
Abstract
We study the self-gravitating Higgs field of a scalar charge. We show that in the zeroth and first approximation in the smallness of the scalar charge, the gravitational field of the scalar charge is described by the Schwarzschild–de Sitter metric with a cosmological constant determined by the vacuum potential of the Higgs field. An equation for the perturbation of the vacuum potential is obtained and studied. Particular exact solutions of the field equation are given. It is shown that in the case of a naked singularity, solutions of the field equation have the character of microscopic oscillations with a Compton wavelength. Asymptotic limit cases of the behavior of solutions are studied and their comparative analysis is carried out in relation to the Fisher solution. The averaging of microscopic oscillations of the scalar field is carried out and it it shown that at (Lambda>0) they make a negative contribution to the macroscopic energy of the scalar field, reducing the observed value of the black hole mass. A computer simulation of a scalar field demonstrates various types of the behavior of solutions.
{"title":"Self-gravitating Higgs field of scalar charge","authors":"Yu. G. Ignat’ev","doi":"10.1134/s0040577924050088","DOIUrl":"https://doi.org/10.1134/s0040577924050088","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the self-gravitating Higgs field of a scalar charge. We show that in the zeroth and first approximation in the smallness of the scalar charge, the gravitational field of the scalar charge is described by the Schwarzschild–de Sitter metric with a cosmological constant determined by the vacuum potential of the Higgs field. An equation for the perturbation of the vacuum potential is obtained and studied. Particular exact solutions of the field equation are given. It is shown that in the case of a naked singularity, solutions of the field equation have the character of microscopic oscillations with a Compton wavelength. Asymptotic limit cases of the behavior of solutions are studied and their comparative analysis is carried out in relation to the Fisher solution. The averaging of microscopic oscillations of the scalar field is carried out and it it shown that at <span>(Lambda>0)</span> they make a negative contribution to the macroscopic energy of the scalar field, reducing the observed value of the black hole mass. A computer simulation of a scalar field demonstrates various types of the behavior of solutions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149337","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}
Pub Date : 2024-05-24DOI: 10.1134/s0040577924050039
Haifeng Wang, Yufeng Zhang
Abstract
We construct a new class of higher-dimensional column-vector loop algebras. Based on it, a method for generating higher-dimensional isospectral–nonisospectral integrable hierarchies is proposed. As an application, we derive a generalized nonisospectral integrable Schrödinger hierarchy that can be reduced to the famous derivative nonlinear Schrödinger equation. By using the higher-dimensional column-vector loop algebras, we obtain an extended isospectral–nonisospectral integrable Schrödinger hierarchy that can be reduced to many classical and new equations, such as the extended nonisospectral derivative nonlinear Schrödinger system, the heat equation, and the Fokker–Planck equation, which has a wide range of applications in stochastic dynamical systems. Furthermore, we deduce a (Z_N^varepsilon) nonisospectral integrable Schrödinger hierarchy, which means that the coupling results are extended to an arbitrary number of components. Additionally, the Hamiltonian structures of these hierarchies are discussed by using the quadratic form trace identity.
{"title":"Generation of higher-dimensional isospectral–nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebras","authors":"Haifeng Wang, Yufeng Zhang","doi":"10.1134/s0040577924050039","DOIUrl":"https://doi.org/10.1134/s0040577924050039","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We construct a new class of higher-dimensional column-vector loop algebras. Based on it, a method for generating higher-dimensional isospectral–nonisospectral integrable hierarchies is proposed. As an application, we derive a generalized nonisospectral integrable Schrödinger hierarchy that can be reduced to the famous derivative nonlinear Schrödinger equation. By using the higher-dimensional column-vector loop algebras, we obtain an extended isospectral–nonisospectral integrable Schrödinger hierarchy that can be reduced to many classical and new equations, such as the extended nonisospectral derivative nonlinear Schrödinger system, the heat equation, and the Fokker–Planck equation, which has a wide range of applications in stochastic dynamical systems. Furthermore, we deduce a <span>(Z_N^varepsilon)</span> nonisospectral integrable Schrödinger hierarchy, which means that the coupling results are extended to an arbitrary number of components. Additionally, the Hamiltonian structures of these hierarchies are discussed by using the quadratic form trace identity. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149295","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}
Pub Date : 2024-05-24DOI: 10.1134/s0040577924050064
Jen-Hsu Chang
Abstract
We construct the parity–time symmetric solitons of the complex KP equation using the totally nonnegative Grassmannian. We obtain that every element in the totally nonnegative orthogonal Grassmannian corresponds to a parity–time symmetric soliton solution.
{"title":"Parity–time symmetric solitons of the complex KP equation","authors":"Jen-Hsu Chang","doi":"10.1134/s0040577924050064","DOIUrl":"https://doi.org/10.1134/s0040577924050064","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We construct the parity–time symmetric solitons of the complex KP equation using the totally nonnegative Grassmannian. We obtain that every element in the totally nonnegative orthogonal Grassmannian corresponds to a parity–time symmetric soliton solution. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149342","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}
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