{"title":"On the blow-up of the solution of a ((1+1))-dimensional thermal–electrical model","authors":"M. V. Artemeva, M. O. Korpusov","doi":"10.1134/S0040577924050040","DOIUrl":"10.1134/S0040577924050040","url":null,"abstract":"<p> We consider a <span>((1+1))</span>-dimensional thermal–electrical model of semiconductor heating in an electric field. For the corresponding initial-boundary value problem, we prove the existence of a classical solution that cannot be continued in time and obtain sufficient conditions for the blow-up of the solution in a finite time. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 2","pages":"748 - 760"},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141134700","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}
{"title":"Self-gravitating Higgs field of scalar charge","authors":"Yu. G. Ignat’ev","doi":"10.1134/S0040577924050088","DOIUrl":"10.1134/S0040577924050088","url":null,"abstract":"<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":"219 2","pages":"792 - 805"},"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}
{"title":"Particle creation in cosmological space–time by a time-varying electric field","authors":"H. Rezki, S. Zaim","doi":"10.1134/S004057792405012X","DOIUrl":"10.1134/S004057792405012X","url":null,"abstract":"<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":"219 2","pages":"856 - 870"},"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}
{"title":"Soliton solutions of the negative-order nonlinear Schrödinger equation","authors":"G. U. Urazboev, I. I. Baltaeva, A. K. Babadjanova","doi":"10.1134/S0040577924050052","DOIUrl":"10.1134/S0040577924050052","url":null,"abstract":"<p> We discuss the integration of the Cauchy problem for the negative-order nonlinear Schrödinger equation in the class of rapidly decreasing functions via the inverse scattering problem method. In particular, we obtain the time dependence of scattering data of the Zakharov–Shabat system with the potential that is a solution of the considered problem. We give an explicit representation of the one-soliton solution of the negative-order nonlinear Schrödinger equation based on the obtained results. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 2","pages":"761 - 769"},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141142326","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}
{"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":"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}
{"title":"On the constrained (q)-mKP hierarchy: Additional symmetry and a hidden Virasoro algebraic structure","authors":"Song Li, Kelei Tian, Ying Xu, 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}
{"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}
{"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}
{"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}
{"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}