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A combined generalized Kaup–Newell soliton hierarchy and its hereditary recursion operator and bi-Hamiltonian structure 广义考普-纽维尔孤子组合层次及其遗传递归算子和双哈密顿结构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1134/S0040577924100027
Wen-Xiu Ma
{"title":"A combined generalized Kaup–Newell soliton hierarchy and its hereditary recursion operator and bi-Hamiltonian structure","authors":"Wen-Xiu Ma","doi":"10.1134/S0040577924100027","DOIUrl":"10.1134/S0040577924100027","url":null,"abstract":"<p> On the basis of a specific matrix Lie algebra, we propose a Kaup–Newell-type matrix eigenvalue problem with four potentials and compute an associated soliton hierarchy within the zero-curvature formulation. A hereditary recursion operator and a bi-Hamiltonian structure are presented to show the Liouville integrability of the resulting soliton hierarchy. An illustrative example is a novel model consisting of combined derivative nonlinear Schrödinger equations with two arbitrary constants. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518793","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 solutions of the quantum scattering problem for binary collisions in a system of three charged particles. The inclusion of the dipole interaction 三个带电粒子系统中二元碰撞的量子散射问题的渐近解。包含偶极相互作用
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1134/S0040577924100106
V. A. Gradusov, S. L. Yakovlev
{"title":"Asymptotic solutions of the quantum scattering problem for binary collisions in a system of three charged particles. The inclusion of the dipole interaction","authors":"V. A. Gradusov,&nbsp;S. L. Yakovlev","doi":"10.1134/S0040577924100106","DOIUrl":"10.1134/S0040577924100106","url":null,"abstract":"<p> We construct asymptotic solutions of the binary scattering problem in a three-particle system with the Coulomb interaction; the solutions explicitly take the induced dipole interaction between a free particle and a bound pair of particles into account in each of the possible configurations. Using these solutions, we formulate boundary conditions for the scattering problem in the system of three charged particles for energies that are below the ionization threshold. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518702","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 three-component KP and three-component mKP hierarchies 三分量 KP 和三分量 mKP 层次之间的量纲变换
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090058
Lin Sun, Chuanzhong Li, Ming Chen, Wei Liu
{"title":"Gauge transformations between three-component KP and three-component mKP hierarchies","authors":"Lin Sun,&nbsp;Chuanzhong Li,&nbsp;Ming Chen,&nbsp;Wei Liu","doi":"10.1134/S0040577924090058","DOIUrl":"10.1134/S0040577924090058","url":null,"abstract":"<p> We examine the gauge transformations between the three-component Kadomtsev–Petviashvili (KP) hierarchy and the three-component modified Kadomtsev–Petviashvili (mKP) hierarchy. We introduce the auto-Bäcklund transformation of the three-component KP hierarchy and describe the Miura transformation of the three-component KP and mKP hierarchies, that is, <span>(k=0to k=1)</span>. Additionally, the auto-Bäcklund transformation of the three-component mKP hierarchy is also given. This provides more powerful evidence that the gauge transformations generate Miura and auto-Bäcklund transformation on the eigenfunctions of the three-component KP and mKP hierarchies. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413491","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
Quasi-Grammian loop dynamics of a multicomponent semidiscrete short pulse equation 多分量半离散短脉冲方程的准格拉米亚环路动力学
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090083
A. Inam, M. ul Hassan
{"title":"Quasi-Grammian loop dynamics of a multicomponent semidiscrete short pulse equation","authors":"A. Inam,&nbsp;M. ul Hassan","doi":"10.1134/S0040577924090083","DOIUrl":"10.1134/S0040577924090083","url":null,"abstract":"<p> A semidiscrete short-pulse equation (sdSPE) is presented via a proposed Lax pair. A multicomponent sdSPE is derived using <span>(2^Mtimes 2^M)</span> Lax matrices. The standard binary Darboux transformation (SBDT) is employed by constructing the Darboux matrices from particular eigenvector solutions of the generalized Lax pair not only in the direct space but also in its adjoint space. Explicit expressions of the first- and second-order nontrivial quasi-Grammian loop solutions of the multicomponent sdSPE are computed, by iterating its SBDT. It is also shown that quasi-Grammian loop solutions reduce to the elementary loop solutions by applying reduction of spectral parameters. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413489","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
Nonlocal symmetries of two 2-component equations of Camassa–Holm type 卡马萨-霍尔姆型两个 2 分量方程的非局部对称性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090046
Ziqi Li, Kai Tian
{"title":"Nonlocal symmetries of two 2-component equations of Camassa–Holm type","authors":"Ziqi Li,&nbsp;Kai Tian","doi":"10.1134/S0040577924090046","DOIUrl":"10.1134/S0040577924090046","url":null,"abstract":"<p> For a <span>(2)</span>-component Camassa–Holm equation, as well as a <span>(2)</span>-component generalization of the modified Camassa–Holm equation, nonlocal infinitesimal symmetries quadratically dependent on eigenfunctions of linear spectral problems are constructed from functional gradients of spectral parameters. With appropriate pseudopotentials, these nonlocal infinitesimal symmetries are prolonged to enlarged systems, and then explicitly integrated to generate symmetry transformations in finite form for the enlarged systems. As implementations of these finite symmetry transformations, some kinds of nontrivial solutions and Bäcklund transformations are derived for both equations. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413615","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
Wave propagation in the Kolmogorov–Petrovsky–Piscounov–Fisher equation with delay 有延迟的 Kolmogorov-Petrovsky-Piscounov-Fisher 方程中的波传播
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090010
S. V. Aleshin, S. D. Glyzin, S. A. Kashchenko
{"title":"Wave propagation in the Kolmogorov–Petrovsky–Piscounov–Fisher equation with delay","authors":"S. V. Aleshin,&nbsp;S. D. Glyzin,&nbsp;S. A. Kashchenko","doi":"10.1134/S0040577924090010","DOIUrl":"10.1134/S0040577924090010","url":null,"abstract":"<p> The problem of density wave propagation is considered for a logistic equation with delay and diffusion. This equation, called the Kolmogorov–Petrovsky–Piscounov–Fisher equation with delay, is investigated by asymptotic and numerical methods. Local properties of solutions corresponding to this equation with periodic boundary conditions are studied. It is shown that an increase in the period leads to the emergence of stable solutions with a more complex spatial structure. The process of wave propagation from one and from two initial perturbations is analyzed numerically, which allows tracing the process of wave interaction in the second case. The complex spatially inhomogeneous structure arising during the wave propagation and interaction can be explained by the properties of the corresponding solutions of a periodic boundary value problem with an increasing range of the spatial variable. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413502","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
Riemann–Hilbert approach to coupled nonlinear Schrödinger equations on a half-line 半线上耦合非线性薛定谔方程的黎曼-希尔伯特方法
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S004057792409006X
Shun Wang, Jian Li
{"title":"Riemann–Hilbert approach to coupled nonlinear Schrödinger equations on a half-line","authors":"Shun Wang,&nbsp;Jian Li","doi":"10.1134/S004057792409006X","DOIUrl":"10.1134/S004057792409006X","url":null,"abstract":"<p> We use the Fokas method to investigate coupled derivative nonlinear Schrödinger equations on a half-line. The solutions are represented in terms of solutions of two matrix Riemann–Hilbert problems (RHPs) formulated in the complex plane of the spectral parameter. The elements of jump matrices are composed of spectral functions and are derived from the initial and boundary values. The spectral functions are not independent of each other, but satisfy a compatibility condition, the so-called global condition. Therefore, if the initial boundary and values and the defined spectral functions satisfy the global condition, the RHP is solvable and hence the derivative nonlinear Schrödinger equations on a half-line are solvable. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413606","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
Boundedness-below conditions for a general scalar potential of two real scalar fields and the Higgs boson 两个实标量场和希格斯玻色子的一般标量势的有界-无界条件
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090101
Yisheng Song, Liqun Qi
{"title":"Boundedness-below conditions for a general scalar potential of two real scalar fields and the Higgs boson","authors":"Yisheng Song,&nbsp;Liqun Qi","doi":"10.1134/S0040577924090101","DOIUrl":"10.1134/S0040577924090101","url":null,"abstract":"<p> The most general scalar potential of two real scalar fields and a Higgs boson is a quartic homogeneous polynomial in three variables, which defines a <span>(4)</span>th-order three-dimensional symmetric tensor. Hence, the boundedness of such a scalar potential from below involves the positive (semi-)definiteness of the corresponding tensor. In this paper, we therefore mainly discuss analytic expressions of positive (semi-)definiteness for such a special tensor. First, an analytically necessary and sufficient condition is given to test the positive (semi-)definiteness of a <span>(4)</span>th-order two-dimensional symmetric tensor. Furthermore, by means of such a result, the analytic necessary and sufficient conditions of the boundedness from below are obtained for a general scalar potential of two real scalar fields and the Higgs boson. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413504","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 positive fixed points of operator of Hammerstein type with degenerate kernel and Gibbs measures 论具有退化核的哈默斯坦型算子的正定点和吉布斯量纲
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090113
I. M. Mavlonov, Kh. N. Khushvaktov, G. P. Arzikulov, F. H. Haydarov
{"title":"On positive fixed points of operator of Hammerstein type with degenerate kernel and Gibbs measures","authors":"I. M. Mavlonov,&nbsp;Kh. N. Khushvaktov,&nbsp;G. P. Arzikulov,&nbsp;F. H. Haydarov","doi":"10.1134/S0040577924090113","DOIUrl":"10.1134/S0040577924090113","url":null,"abstract":"<p> It is known that translation-invariant Gibbs measures of a model with an uncountable set of spin values can be described by positive fixed points of a nonlinear integral operator of Hammerstein type. Significant results have been obtained on positive fixed points of a Hammerstein-type operator with a degenerate kernel, but the existence of Gibbs measures corresponding to the fixed points have not been proved for constructed kernels. We construct new degenerate kernels of the Hammerstein operator in the context of the theory of Gibbs measures, and show that each positive fixed point of the operator gives a translation-invariant Gibbs measure. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413443","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 solution of the problem of the interaction between a point charge and an insulator with nonlinear susceptibility 点电荷与具有非线性易感性的绝缘体之间相互作用问题的精确解答
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090095
A. A. Belov, M. A. Tintul, P. A. Polyakov
{"title":"Exact solution of the problem of the interaction between a point charge and an insulator with nonlinear susceptibility","authors":"A. A. Belov,&nbsp;M. A. Tintul,&nbsp;P. A. Polyakov","doi":"10.1134/S0040577924090095","DOIUrl":"10.1134/S0040577924090095","url":null,"abstract":"<p> We construct a new exact solution of the problem of a filament placed parallel to the interface between two insulators, one of which has a nonlinear susceptibility. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413611","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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