Pub Date : 2024-07-27DOI: 10.1134/s0040577924070110
V. M. Rothos
Abstract
We consider a defocusing Manakov system (vector nonlinear Schrödinger (NLS) system) with nonvanishing boundary conditions and use the inverse scattering transform formalism. Integrable models provide a very useful proving ground for testing new analytic and numerical approaches to studying the vector NLS system. We develop a perturbation theory for the integrable vector NLS model. Evidently, small disturbance of the integrability condition can be considered a perturbation of the integrable model. Our formalism is based on the Riemann–Hilbert problem associated with the vector NLS model with nonvanishing boundary conditions. We use the RH and adiabatic perturbation theory to analyze the dynamics of dark–dark and dark–bright solitons in the presence of a perturbation with nonvanishing boundary conditions.
{"title":"Adiabatic perturbation theory for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions","authors":"V. M. Rothos","doi":"10.1134/s0040577924070110","DOIUrl":"https://doi.org/10.1134/s0040577924070110","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a defocusing Manakov system (vector nonlinear Schrödinger (NLS) system) with nonvanishing boundary conditions and use the inverse scattering transform formalism. Integrable models provide a very useful proving ground for testing new analytic and numerical approaches to studying the vector NLS system. We develop a perturbation theory for the integrable vector NLS model. Evidently, small disturbance of the integrability condition can be considered a perturbation of the integrable model. Our formalism is based on the Riemann–Hilbert problem associated with the vector NLS model with nonvanishing boundary conditions. We use the RH and adiabatic perturbation theory to analyze the dynamics of dark–dark and dark–bright solitons in the presence of a perturbation with nonvanishing boundary conditions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775697","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 : 2024-07-27DOI: 10.1134/s0040577924070079
N. T. Levashova, E. A. Chunzhuk, A. O. Orlov
Abstract
We study the autowave front propagation in a medium with discontinuous characteristics and the conditions for its stabilization to a stationary solution with a large gradient at the interface between media in the one-dimensional case. The asymptotic method of differential inequalities, based on constructing an asymptotic approximation of the solution, is the main method of study. We develop an algorithm for constructing such an approximation for the solution of the moving front form in a medium with discontinuous characteristics. The application of such an algorithm requires a detailed analysis of the behavior of the solution in neighborhoods of two singular points: the front localization point and the medium discontinuity point. As a result, we obtain a system of equations for the front propagation speed; this distinguishes this paper from the previously published ones. The developed algorithm can be used to describe autowave propagation in layered media. The results can also be extended to the multidimensional case.
{"title":"Stabilization of the front in a medium with discontinuous characteristics","authors":"N. T. Levashova, E. A. Chunzhuk, A. O. Orlov","doi":"10.1134/s0040577924070079","DOIUrl":"https://doi.org/10.1134/s0040577924070079","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the autowave front propagation in a medium with discontinuous characteristics and the conditions for its stabilization to a stationary solution with a large gradient at the interface between media in the one-dimensional case. The asymptotic method of differential inequalities, based on constructing an asymptotic approximation of the solution, is the main method of study. We develop an algorithm for constructing such an approximation for the solution of the moving front form in a medium with discontinuous characteristics. The application of such an algorithm requires a detailed analysis of the behavior of the solution in neighborhoods of two singular points: the front localization point and the medium discontinuity point. As a result, we obtain a system of equations for the front propagation speed; this distinguishes this paper from the previously published ones. The developed algorithm can be used to describe autowave propagation in layered media. The results can also be extended to the multidimensional case. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775761","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 : 2024-07-27DOI: 10.1134/s0040577924070080
P. N. Nesterov, J. I. Stavroulakis
Abstract
We study the oscillation of a first-order delay equation with negative feedback at the critical threshold (1/e). We apply a novel center manifold method, proving that the oscillation of the delay equation is equivalent to the oscillation of a (2)-dimensional system of ordinary differential equations (ODEs) on the center manifold. It is well known that the delay equation oscillation is equivalent to the oscillation of a certain second-order ODE, and we furthermore show that the center manifold system is asymptotically equivalent to this same second-order ODE. In addition, the center manifold method has the advantage of being applicable to the case where the parameters oscillate around the critical value (1/e), thereby extending and refining previous results in this case.
{"title":"Triple equivalence of the oscillatory behavior for scalar delay differential equations","authors":"P. N. Nesterov, J. I. Stavroulakis","doi":"10.1134/s0040577924070080","DOIUrl":"https://doi.org/10.1134/s0040577924070080","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the oscillation of a first-order delay equation with negative feedback at the critical threshold <span>(1/e)</span>. We apply a novel center manifold method, proving that the oscillation of the delay equation is equivalent to the oscillation of a <span>(2)</span>-dimensional system of ordinary differential equations (ODEs) on the center manifold. It is well known that the delay equation oscillation is equivalent to the oscillation of a certain second-order ODE, and we furthermore show that the center manifold system is asymptotically equivalent to this same second-order ODE. In addition, the center manifold method has the advantage of being applicable to the case where the parameters oscillate around the critical value <span>(1/e)</span>, thereby extending and refining previous results in this case. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775694","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/s0040577924060035
Dan Wang
Abstract
We analyze the asymptotic behavior of the Hankel determinant generated by a semiclassical Laguerre weight. For this, we use ladder operators and track the evolution of parameters to establish that an auxiliary quantity associated with the semiclassical Laguerre weight satisfies the Painlevé IV equation, subject to suitable transformations of variables. Using the Coulomb fluid method, we derive the large-(n) expansion of the logarithmic form of the Hankel determinant. This allows us to gain insights into the scaling and fluctuations of the determinant, providing a deeper understanding of its behavior in the semiclassical Laguerre ensemble. Moreover, we delve into the asymptotic evaluation of monic orthogonal polynomials with respect to the semiclassical Laguerre weight, focusing on a special case. In doing so, we shed light on the properties and characteristics of these polynomials in the context of the ensemble. Furthermore, we explore the relation between the second-order differential equations satisfied by the monic orthogonal polynomials with respect to the semiclassical Laguerre weight and the tri-confluent Heun equations or the bi-confluent Heun equations.
摘要 我们分析了由半经典拉盖尔权重生成的汉克尔行列式的渐近行为。为此，我们使用梯形算子并跟踪参数的演化，以确定与半经典拉盖尔权重相关的辅助量在适当的变量变换下满足潘列韦 IV 方程。利用库仑流体方法，我们推导出汉克尔行列式对数形式的大（n）展开。这使我们能够深入了解行列式的缩放和波动，从而更深入地理解它在半经典拉盖尔集合中的行为。此外，我们还深入研究了单次正交多项式相对于半经典拉盖尔权重的渐近评估，并将重点放在一个特例上。在此过程中，我们揭示了这些多项式在集合背景下的性质和特征。此外，我们还探讨了关于半经典拉盖尔权重的单正交多项式所满足的二阶微分方程与三汇合海恩方程或双汇合海恩方程之间的关系。
{"title":"The Hankel determinant for a semiclassical Laguerre unitary ensemble, Painlevé IV and Heun equations","authors":"Dan Wang","doi":"10.1134/s0040577924060035","DOIUrl":"https://doi.org/10.1134/s0040577924060035","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We analyze the asymptotic behavior of the Hankel determinant generated by a semiclassical Laguerre weight. For this, we use ladder operators and track the evolution of parameters to establish that an auxiliary quantity associated with the semiclassical Laguerre weight satisfies the Painlevé IV equation, subject to suitable transformations of variables. Using the Coulomb fluid method, we derive the large-<span>(n)</span> expansion of the logarithmic form of the Hankel determinant. This allows us to gain insights into the scaling and fluctuations of the determinant, providing a deeper understanding of its behavior in the semiclassical Laguerre ensemble. Moreover, we delve into the asymptotic evaluation of monic orthogonal polynomials with respect to the semiclassical Laguerre weight, focusing on a special case. In doing so, we shed light on the properties and characteristics of these polynomials in the context of the ensemble. Furthermore, we explore the relation between the second-order differential equations satisfied by the monic orthogonal polynomials with respect to the semiclassical Laguerre weight and the tri-confluent Heun equations or the bi-confluent Heun equations. </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":"141503132","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/s0040577924060023
N. G. Marchuk
Abstract
We introduce a new equation (a class of equations) to be considered as a candidate for the equation for a nonzero-mass neutrino.
摘要 我们引入了一个新方程（一类方程），作为非零质量中微子方程的候选方程。
{"title":"A class of field equations for neutrinos with nonzero masses","authors":"N. G. Marchuk","doi":"10.1134/s0040577924060023","DOIUrl":"https://doi.org/10.1134/s0040577924060023","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We introduce a new equation (a class of equations) to be considered as a candidate for the equation for a nonzero-mass neutrino. </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":"141503133","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/s0040577924060072
V. A. Smirnov
Abstract
We show how the well-known large-mass expansion of Feynman integrals can be simplified to obtain more terms of the expansion in analytic form. Expansion of two-loop four-point Feynman integrals that contribute to the (H to ggg) process is used as an example.
摘要 我们展示了如何简化著名的费曼积分大质量展开，以得到更多的解析形式的展开项。以有助于(H to ggg) 过程的二环四点费曼积分展开为例。
{"title":"Simplifying the large-mass expansion of Feynman integrals","authors":"V. A. Smirnov","doi":"10.1134/s0040577924060072","DOIUrl":"https://doi.org/10.1134/s0040577924060072","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We show how the well-known large-mass expansion of Feynman integrals can be simplified to obtain more terms of the expansion in analytic form. Expansion of two-loop four-point Feynman integrals that contribute to the <span>(H to ggg)</span> process is used as an example. </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":"141514123","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/s0040577924060047
Qi Li, Qiu-yuan Duan
Abstract
A hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources is introduced. The physically significant nonlinear equation is associated with the AKNS spectral problem. In the nonlocal case, the squared eigenfunction of the (L) operator leads to some changes in the term of the source that affect the motion of solitons. The soliton solutions of the nonlocal nonlinear Schrödinger equation with self-consistent sources are presented using the inverse scattering transform. The dynamics of the solitons are illustrated, which differ from those of the nonlocal equation without a source.
{"title":"A hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources and dynamics","authors":"Qi Li, Qiu-yuan Duan","doi":"10.1134/s0040577924060047","DOIUrl":"https://doi.org/10.1134/s0040577924060047","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources is introduced. The physically significant nonlinear equation is associated with the AKNS spectral problem. In the nonlocal case, the squared eigenfunction of the <span>(L)</span> operator leads to some changes in the term of the source that affect the motion of solitons. The soliton solutions of the nonlocal nonlinear Schrödinger equation with self-consistent sources are presented using the inverse scattering transform. The dynamics of the solitons are illustrated, which differ from those of the nonlocal equation without a source. </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":"141503134","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/s0040577924060114
M. M. Rakhmatullaev, B. M. Isakov
Abstract
We consider a mixed-type model given by the three-state Ising–Potts model on a Cayley tree. A criterion for the existence of limit Gibbs measures for this model on an arbitrary-order Cayley tree is obtained. Translation-invariant Gibbs measures on a second-order Cayley tree are studied. The existence of a phase transition is proved: a range of parameter values is found in which there are one to seven Gibbs measures for the three-state Ising–Potts model.
{"title":"Translation-invariant Gibbs measures for the Ising–Potts model on a second-order Cayley tree","authors":"M. M. Rakhmatullaev, B. M. Isakov","doi":"10.1134/s0040577924060114","DOIUrl":"https://doi.org/10.1134/s0040577924060114","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a mixed-type model given by the three-state Ising–Potts model on a Cayley tree. A criterion for the existence of limit Gibbs measures for this model on an arbitrary-order Cayley tree is obtained. Translation-invariant Gibbs measures on a second-order Cayley tree are studied. The existence of a phase transition is proved: a range of parameter values is found in which there are one to seven Gibbs measures for the three-state Ising–Potts model. </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":"141514127","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/s0040577924060084
A. V. Balandin
Abstract
We consider chiral-type systems admitting a Lax representation with values in a real or complex semisimple Lie algebra such that an additional regularity condition is satisfied (one of the matrices is a regular element of the Lie algebra). We prove that for a chiral-type system with vanishing torsion and a nonvanishing curvature, the existence of at least one pointwise cosymmetry is a necessary condition for the regular Lax representation.
{"title":"Cosymmetries of chiral-type systems","authors":"A. V. Balandin","doi":"10.1134/s0040577924060084","DOIUrl":"https://doi.org/10.1134/s0040577924060084","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider chiral-type systems admitting a Lax representation with values in a real or complex semisimple Lie algebra such that an additional regularity condition is satisfied (one of the matrices is a regular element of the Lie algebra). We prove that for a chiral-type system with vanishing torsion and a nonvanishing curvature, the existence of at least one pointwise cosymmetry is a necessary condition for the regular Lax representation. </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":"141514124","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/s0040577924060059
Song-lin Zhao, Ke Yan, Ying-ying Sun
Abstract
Solutions of all Adler–Bobenko–Suris equations except (Q4), and of several lattice Boussinesq-type equations are reconsidered by using the Cauchy matrix approach. By introducing a “fake” nonautonomous plane-wave factor, we derive soliton solutions, oscillatory solutions, and semi-oscillatory solutions of the target lattice equations. Unlike the conventional soliton solutions, the oscillatory solutions take constant values on all elementary quadrilaterals on (mathbb{Z}^2), which demonstrates a periodic structure.
{"title":"Revisiting solutions of the Adler–Bobenko–Suris lattice equations and lattice Boussinesq-type equations","authors":"Song-lin Zhao, Ke Yan, Ying-ying Sun","doi":"10.1134/s0040577924060059","DOIUrl":"https://doi.org/10.1134/s0040577924060059","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Solutions of all Adler–Bobenko–Suris equations except <span>(Q4)</span>, and of several lattice Boussinesq-type equations are reconsidered by using the Cauchy matrix approach. By introducing a “fake” nonautonomous plane-wave factor, we derive soliton solutions, oscillatory solutions, and semi-oscillatory solutions of the target lattice equations. Unlike the conventional soliton solutions, the oscillatory solutions take constant values on all elementary quadrilaterals on <span>(mathbb{Z}^2)</span>, which demonstrates a periodic structure. </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":"141514121","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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