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Generation of higher-dimensional isospectral–nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebras 生成与一类新的高维列向量环代数相关的高维等谱-非等谱可积分层次结构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050039
Haifeng Wang, Yufeng Zhang
{"title":"Generation of higher-dimensional isospectral–nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebras","authors":"Haifeng Wang,&nbsp;Yufeng Zhang","doi":"10.1134/S0040577924050039","DOIUrl":"10.1134/S0040577924050039","url":null,"abstract":"<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":"219 2","pages":"722 - 747"},"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}
引用次数: 0
On the constrained (q)-mKP hierarchy: Additional symmetry and a hidden Virasoro algebraic structure 关于受约束的 $$q$$-mKP 层次结构：附加对称性和隐藏的维拉索罗代数结构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050076
Song Li, Kelei Tian, Ying Xu, Ge Yi
{"title":"On the constrained (q)-mKP hierarchy: Additional symmetry and a hidden Virasoro algebraic structure","authors":"Song Li,&nbsp;Kelei Tian,&nbsp;Ying Xu,&nbsp;Ge Yi","doi":"10.1134/S0040577924050076","DOIUrl":"10.1134/S0040577924050076","url":null,"abstract":"<p> We construct the additional symmetry of the constrained <span>(q)</span>-mKP hierarchy. The new modified operator is introduced. The flows and additional flows acting on the modified operator are given. The additional flows acting on the eigenfunction and the adjoint eigenfunction are presented. The hidden Virasoro algebraic structure in the additional symmetry of the constrained <span>(q)</span>-mKP hierarchy is given. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 2","pages":"781 - 791"},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141138234","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
Parity–time symmetric solitons of the complex KP equation 复 KP 方程的奇偶时对称孤子
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050064
Jen-Hsu Chang
{"title":"Parity–time symmetric solitons of the complex KP equation","authors":"Jen-Hsu Chang","doi":"10.1134/S0040577924050064","DOIUrl":"10.1134/S0040577924050064","url":null,"abstract":"<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":"219 2","pages":"770 - 780"},"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}
引用次数: 0
On the properties of solutions of a system of two nonlinear differential equations associated with the Josephson model 论与约瑟夫森模型相关的两个非线性微分方程系的解的性质
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI: 10.1134/S0040577924040020
V. V. Tsegelnik
{"title":"On the properties of solutions of a system of two nonlinear differential equations associated with the Josephson model","authors":"V. V. Tsegelnik","doi":"10.1134/S0040577924040020","DOIUrl":"10.1134/S0040577924040020","url":null,"abstract":"<p> We investigate the analytic properties of solutions of a system of two first-order nonlinear differential equations with an arbitrary parameter <span>(l)</span> associated with an overdamped Josephson model. We reduce this system to a system of differential equations that is equivalent to the fifth Painlevé equation with the sets of parameters </p><p> We show that the solution of the third Painlevé equation with the parameters <span>((-2l, 2l-2,1,-1))</span> can be represented as the ratio of two linear fractional transformations of the solutions of the fifth Painlevé equation (with the parameters in the above sequence) connected by a Bäcklund transformation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 1","pages":"539 - 543"},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800835","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
The focusing coupled modified Korteweg–de Vries equation with nonzero boundary conditions: the Riemann–Hilbert problem and soliton classification 具有非零边界条件的聚焦耦合修正科特韦格-德-弗里斯方程：黎曼-希尔伯特问题与孤子分类
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI: 10.1134/S004057792404007X
Xinxin Ma
{"title":"The focusing coupled modified Korteweg–de Vries equation with nonzero boundary conditions: the Riemann–Hilbert problem and soliton classification","authors":"Xinxin Ma","doi":"10.1134/S004057792404007X","DOIUrl":"10.1134/S004057792404007X","url":null,"abstract":"<p> The focusing coupled modified Korteweg–de Vries equation with nonzero boundary conditions is investigated by the Riemann–Hilbert approach. Three symmetries are formulated to derive compact exact solutions. The solutions include six different types of soliton solutions and breathers, such as dark–dark, bright–bright, kink–dark–dark, kink–bright–bright solitons, and a breather–breather solution. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 1","pages":"598 - 628"},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800619","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
Diffusion of a collisionless gas 无碰撞气体的扩散
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI: 10.1134/S004057792404010X
V. V. Kozlov
{"title":"Diffusion of a collisionless gas","authors":"V. V. Kozlov","doi":"10.1134/S004057792404010X","DOIUrl":"10.1134/S004057792404010X","url":null,"abstract":"<p> We study a diffusion-type equation for the density of a collisionless relativistic gas (Jüttner gas). The rate of diffusion propagation turns out to be finite. We consider problems of the existence and uniqueness of solutions of this equation, as well as some of its generalized solutions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 1","pages":"663 - 672"},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800694","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 existence of certain elliptic solutions of the cubically nonlinear Schrödinger equation 论立方非线性薛定谔方程某些椭圆解的存在性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI: 10.1134/S0040577924040044
H. W. Schürmann, V. S. Serov
{"title":"On the existence of certain elliptic solutions of the cubically nonlinear Schrödinger equation","authors":"H. W. Schürmann,&nbsp;V. S. Serov","doi":"10.1134/S0040577924040044","DOIUrl":"10.1134/S0040577924040044","url":null,"abstract":"<p> We consider solutions of the cubically nonlinear Schrödinger equation. For a certain class of solutions of the form <span>(Psi(t,z)=(f(t,z)+id(z))e^{iphi(z)})</span> with <span>(f,phi,dinmathbb{R})</span>, we prove that they are nonexistent in the general case <span>(f_zneq 0)</span>, <span>(f_tneq 0)</span>, <span>(d_zneq 0)</span>. In the three nongeneric cases (<span>(f_zneq 0)</span>), (<span>(f_tneq 0)</span>, <span>(f_t=0)</span>, <span>(d_z=0)</span>), and (<span>(f_z=0)</span>, <span>(f_tneq 0)</span>), we present a two-parameter set of solutions, for which we find the constraints specifying real bounded and unbounded solutions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 1","pages":"557 - 566"},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800541","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
Solitons in a semi-infinite ferromagnet with anisotropy of the easy axis type 具有易轴型各向异性的半无限铁磁体中的孤子
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI: 10.1134/S0040577924040068
V. V. Kiselev
{"title":"Solitons in a semi-infinite ferromagnet with anisotropy of the easy axis type","authors":"V. V. Kiselev","doi":"10.1134/S0040577924040068","DOIUrl":"10.1134/S0040577924040068","url":null,"abstract":"<p> We propose a special variant of the inverse scattering transform method to construct and analyze soliton excitations in a semi-infinite sample of an easy-axis ferromagnet in the case of a partial pinning of spins at its surface. We consider the limit cases of free edge spins and spins that are fully pinned at the sample boundary. We find frequency and modulation characteristics of solitons localized near the sample surface. In the case of different degrees of edge spin pinning, we study changes in the cores of moving solitons as a result of their elastic reflection from the sample boundary. We obtain integrals of motion that control the dynamics of magnetic solitons in a semi-infinite sample. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 1","pages":"576 - 597"},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800532","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
Cauchy problem for a nonlinear Schrödinger equation with a large initial gradient in the weakly dispersive limit 弱色散极限下具有大初始梯度的非线性薛定谔方程的考奇问题
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI: 10.1134/S0040577924040019
S. V. Zakharov
{"title":"Cauchy problem for a nonlinear Schrödinger equation with a large initial gradient in the weakly dispersive limit","authors":"S. V. Zakharov","doi":"10.1134/S0040577924040019","DOIUrl":"10.1134/S0040577924040019","url":null,"abstract":"<p> We consider the Cauchy problem for the cubic nonlinear Schrödinger equation with a large gradient of the initial function and a small dispersion parameter. The renormalization method is used to construct an asymptotic solution in the explicit form of integral convolution. An asymptotic analogue of the renormalization group property is established under scaling transformations determined by the dispersion parameter. In the case of a negative focusing coefficient, a clarifying expression is obtained for the asymptotic solution in terms of known elliptic special functions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 1","pages":"531 - 538"},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800616","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
Similarity of cosmological models and its application to the analysis of cosmological evolution 宇宙学模型的相似性及其在宇宙学演化分析中的应用
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI: 10.1134/S0040577924040123
Yu. G. Ignat’ev
{"title":"Similarity of cosmological models and its application to the analysis of cosmological evolution","authors":"Yu. G. Ignat’ev","doi":"10.1134/S0040577924040123","DOIUrl":"10.1134/S0040577924040123","url":null,"abstract":"<p> Scale transformations of cosmological models based on a statistical system of degenerate fermions with a scalar Higgs interaction are studied. The similarity properties of cosmological models under scale transformations of their fundamental parameters are revealed. The transformation laws for the coordinates of singular points and eigenvalues of the characteristic matrix of the dynamical system of the cosmological model under its scale transformations are established. With the help of the transformation to new variables, the previously studied dynamical system of scalar-charged fermions is modified to a dynamical system with a nondegenerate characteristic matrix; for its nondegenerate branch, the singular points and eigenvalues of the characteristic matrix are found, which coincide with the corresponding values for the vacuum field model. Examples of numerical simulation of such cosmological models are given. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 1","pages":"688 - 703"},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800811","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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