Theoretical and Mathematical Physics最新文献

Review of exact solutions and reductions of Monge–Ampère type equations monge - ampantere型方程的精确解与约简

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090028

A. V. Aksenov, A. D. Polyanin

{"title":"Review of exact solutions and reductions of Monge–Ampère type equations","authors":"A. V. Aksenov, A. D. Polyanin","doi":"10.1134/S0040577925090028","DOIUrl":"10.1134/S0040577925090028","url":null,"abstract":" We present a review of publications devoted to exact solutions, transformations, symmetries, reductions, and applications of strongly nonlinear stationary and nonstationary (parabolic) equations of the Monge–Ampère type. We study the strongly nonlinear nonstationary mathematical physics equations with three independent variables that contain a quadratic combination of second spatial derivatives of the Monge–Ampère type and an arbitrary degree of the first temporal derivative or an arbitrary function depending on this derivative. We study the symmetries of these equations using group analysis methods. We derive formulas that enable the construction of multiparameter families of solutions, based on simpler solutions. We consider two-dimensional and one-dimensional symmetry and nonsymmetry reductions, which transform the original equations into simpler partial differential equations with two independent variables, or to ordinary differential equations and systems of such equations. Self-similar and other invariant solutions are described. Using generalized and functional separation of variables methods, we constructed several new exact solutions, many of which are expressed in elementary functions or in quadratures. Some solutions are obtained using auxiliary intermediate-point or contact transformations. These exact solutions can be used as test problems to verify the adequacy of and evaluate the accuracy of numerical and approximate analytical methods for solving problems described by strongly nonlinear mathematical physics equations. ","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 3","pages":"1527 - 1566"},"PeriodicalIF":1.1,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170023","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

Solution of double and triple sine-Gordon equations 二重和三重正弦戈登方程的解

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090089

Yu. V. Pavlov

引用次数: 0

Formation of the region of phase transformations in the case of the conversion of CH(_4) hydrate into CO(_2) hydrate in a porous medium 多孔介质中CH (_4)水合物转化为CO (_2)水合物时相变区域的形成

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090119

G. G. Tsypkin

{"title":"Formation of the region of phase transformations in the case of the conversion of CH(_4) hydrate into CO(_2) hydrate in a porous medium","authors":"G. G. Tsypkin","doi":"10.1134/S0040577925090119","DOIUrl":"10.1134/S0040577925090119","url":null,"abstract":" We study the problem with an unknown moving boundary of the conversion of (mathrm{CH}_4) hydrate into (mathrm{CO}_2) hydrate in a porous medium. We assume that in the initial state, methane hydrate coexists with water and free methane in the thermodynamic equilibrium state. Calculations show that the assumptions of the existence of the front conversion mode and of the constancy of saturations before the front in the mathematical model lead to the methane hydrate supercooling. We propose a generalized mathematical model that takes into account phase transitions in an extended region before the front. We find a self-similar solution of the problem in the linear approximation. Our made calculations show that the carbon dioxide injection with the conversion of methane hydrate into carbon dioxide hydrate is accompanied by the formation of methane hydrate before the front. We show that an amount of formed methane hydrate before the front increases with increasing injection pressure and permeability. We find that the hydrate formation in the mixture region increases the conversion front velocity. ","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 3","pages":"1671 - 1680"},"PeriodicalIF":1.1,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169636","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

Generalized nonlinear Schrödinger equation for longitudinal deformation waves in an acoustic metamaterial 声学超材料纵向变形波的广义非线性Schrödinger方程

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090107

A. V. Porubov

引用次数: 0

Asymptotics of the Evans function for subsonic solitary waves in a micropolar electrically conductive elastic medium 微极导电弹性介质中亚音速孤波的Evans函数渐近性

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090065

V. I. Erofeev, A. T. Il’ichev, V. Ya. Tomashpolskii

引用次数: 0

Shanks extrapolation method and exact solutions of equations of nonlinear mathematical physics Shanks外推法与非线性数学物理方程的精确解

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090120

A. I. Zemlyanukhin, A. V. Bochkarev, Yu. A. Blinkov

引用次数: 0

Discontinuity structures in a micropolar magnetoelastic medium and methods for studying discontinuities in models with dispersion and a finite velocity of the wave propagation 微极磁弹性介质中的不连续结构以及具有频散和有限波传播速度的模型中不连续结构的研究方法

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S004057792509003X

I. B. Bakholdin

{"title":"Discontinuity structures in a micropolar magnetoelastic medium and methods for studying discontinuities in models with dispersion and a finite velocity of the wave propagation","authors":"I. B. Bakholdin","doi":"10.1134/S004057792509003X","DOIUrl":"10.1134/S004057792509003X","url":null,"abstract":" We consider solutions of a system of magnetoelasticity equations. As initial data for these solutions, we use data of the smoothed step type (the problem of discontinuity decay). Among these solutions, there are solutions with purely nondissipative structures of the soliton type and structures with the radiated wave and the internal dissipative discontinuities of derivatives. We develop techniques for studying discontinuities in solutions of equations with dispersion and finite of wave propagation velocity. We analyze and justify the existence of such structures by studying equations of traveling waves. We reveal the presence of sequences of weak discontinuities in structures with the radiated wave. We also study a dissipative structure of the shock-wave type. We consider conditions for discontinuities and their evolutionary properties. We establish that when studying the discontinuities in the solutions of dispersion equations, the limiting velocities of short waves play the same role as the characteristic velocities for hyperbolic equations. ","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 3","pages":"1567 - 1581"},"PeriodicalIF":1.1,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170025","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

Minimal algebraic solutions of the sixth Painlevé equation 第六阶painlevleve方程的最小代数解

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090053

R. Conte

引用次数: 0

Analytical properties of the spectral problem for the internal gravity waves equation with shear flows under critical wave generation modes 临界波发生模式下具有剪切流的内重力波方程谱问题的解析性质

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090041

V. V. Bulatov

引用次数: 0

Quantum calculus of Fibonacci divisors and Fermion–Boson entanglement for infinite hierarchy of (N=2) supersymmetric golden oscillators 无限层(N=2)超对称金振子的斐波那契除数和费米-玻色子纠缠量子演算

IF 1.1 4区物理与天体物理

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090077

O. K. Pashaev

{"title":"Quantum calculus of Fibonacci divisors and Fermion–Boson entanglement for infinite hierarchy of (N=2) supersymmetric golden oscillators","authors":"O. K. Pashaev","doi":"10.1134/S0040577925090077","DOIUrl":"10.1134/S0040577925090077","url":null,"abstract":" The quantum calculus with two bases, represented by powers of the golden and silver ratios, relates the Fibonacci divisor derivative with Binet formula for the Fibonacci divisor number operator, acting in the Fock space of quantum states. It provides a tool to study the hierarchy of golden oscillators with energy spectrum in the form of Fibonacci divisor numbers. We generalize this model to the supersymmetric number operator and corresponding Binet formula for the supersymmetric Fibonacci divisor number operator. The operator determines Hamiltonian of the hierarchy of supersymmetric golden oscillators, acting in fermion–boson Hilbert space and belonging to (N=2) supersymmetric algebra. The eigenstates of the super Fibonacci divisor number operator are double degenerate and can be characterized by a point on the super-Bloch sphere. By introducing the supersymmetric Fibonacci divisor annihilation operator, we construct the hierarchy of supersymmetric coherent states as eigenstates of this operator. The entanglement of fermions with bosons in these states is calculated by the concurrence, represented as the Gram determinant and expressed in terms of the hierarchy of golden exponential functions. We show that the reference states and the corresponding von Neumann entropy measuring the fermion–boson entanglement are characterized completely by powers of the golden ratio. We give a geometrical classification of entangled states by the Frobenius ball and interpret the concurrence as the double area of a parallelogram in a Hilbert space. ","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 3","pages":"1625 - 1643"},"PeriodicalIF":1.1,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169586","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