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Multiperiodic Solution of the Initial-Boundary Value Problem for an Integro-Differential Equation of the Parabolic Type
AbstractThis paper investigates the initial-boundary value problem for an integro-differential equation of parabolic type with a differentiation...
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Multiperiodic Solutions of Systems of the Equations with Differential Operator in the Direction of a Vector Field
AbstractThe system of the equations with differential operator in the directions of a multiperiodic potential vector field are considered. The...
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Multiperiodic Bounded Oscillations in Quasilinear Finite-Hereditary Integro-Differential Systems Convection-Diffusion Type
AbstractThe question of the existence of multiperiodic oscillations in linear and quasilinear systems describing finitely hereditary processes of the...
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Integrability and Exact Solutions of the (2+1)-dimensional KdV Equation with Bell Polynomials Approach
In this paper, the bilinear formalism, bilinear Bäcklund transformations and Lax pair of the (2+1)-dimensional KdV equation are constructed by the...
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Reduction of a Linear \(\boldsymbol{D_{e}}\)-System to a Canonical Form in the Case of Equivalence to a \(\boldsymbol{D_{e}}\)-System of Higher Order Linear Equations
AbstractIn the article a method of reducing a linear system with a differentiation operator in the direction of the main diagonal to a canonical form...
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Numerical approximation of the scattering amplitude in elasticity
We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions
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Rusanov’s Third-Order Accurate Scheme for Modeling Plasma Oscillations
AbstractA modification of the well-known Rusanov third-order accurate scheme is proposed for modeling nonrelativistic oscillations of a cold plasma....
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Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation
In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo–Fabrizio fractional derivative by dividing the total...
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Live load matrix recovery from scattering data in linear elasticity
We study the numerical approximation of the inverse scattering problem in the two-dimensional homogeneous isotropic linear elasticity with an unknown...
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Chaos
Chaos is ubiquitous. Chaotic motions are unpredictable. Quantifying chaos is a central issue for understanding chaotic phenomena. Experimental...
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Integration of a Linear Equation with Differential Operator, Corresponding to the Main Diagonal in the Space of Independent Variables, and Coefficients, Constant on the Diagonal
We consider an n -th order linear equation with differential operator corresponding to the direction of the main diagonal in the space of independent...
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Function Theories in Cayley-Dickson Algebras and Number Theory
In the recent years a lot of effort has been made to extend the theory of hyperholomorphic functions from the setting of associative Clifford...
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Application of the Energy Conservation Law in the Cold Plasma Model
AbstractFor the two-fluid hydrodynamic cold plasma model, differential relations characterizing the energy conservation law are derived. The case...
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Multiperiodic Solution of a Boundary-Value Problem for one Class of Parabolic Equations with Multidimensional Time
We study the existence and uniqueness of the multiperiodic solution of the first boundary-value problem for a system of parabolic equations with...
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Rational integrability of trigonometric polynomial potentials on the flat torus
We consider a lattice ℒ ⊂ ℝ n and a trigonometric potential V with frequencies k ∈ ℒ. We then prove a strong rational integrability condition on V ,...
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Problem Without Initial Conditions for a Countable System of Semilinear Hyperbolic Equations of the First Order
We derive sufficient conditions for the solvability of the problem without initial conditions for a countable hyperbolic system of semilinear...
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Bilinear approach to quasi-periodic wave solutions of the Kersten-Krasil’shchik coupled KdV-mKdV system
The Hirato bilinear method is extended to construct quasi-periodic wave solutions for the Kersten-Krasil’shchik coupled KdV-mKdV system. One- and...
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Quasi-periodic wave solutions and asymptotic behavior for an extended \((2+1)\)-dimensional shallow water wave equation
Based on Riemann theta function and bilinear Bäcklund transformation, quasi-periodic wave solutions are constructed for an extended
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