Related papers: On Conditionally Invariant Solutions of Magnetohyd…
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…
In this paper, we revisit the governing equations for linear magnetohydrodynamic (MHD) waves and instabilities existing within a magnetized, plane-parallel, self-gravitating slab. Our approach allows for fully non-uniformly magnetized…
In this article we study the long-time behaviour of a system of nonlinear Partial Differential Equations (PDEs) modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We…
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface…
The present paper is devoted to existence results for time-periodic solutions of generalized nonlinear wave equations in a closed Riemannian manifold M. Our main focus lies on the doubly degenerate setting where the associated generalized…
The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretical, symmetry analysis construct wide families of classical…
In this paper, we present exact divergence-free spectral method for solving the incompressible and resistive magneto-hydrodynamic (MHD) equations in two and three dimensions, as well as the efficient solution algorithm and unconditionally…
To solve MHD problems within the framework of the theory of two-scale mean fields, it is important to study the invariants of magnetic lines. Such invariants are constructed on the basis of invariants of classical links, which must satisfy…
The well-known "Sommerfeld radiation problem" of a small -Hertzian- vertical dipole above flat lossy ground is reconsidered. The problem is examined in the spectral domain, through which it is proved to yield relatively simple integral…
Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which…
We identify a generic class of two dimensional nonstandard Hamiltonian systems which exhibit isochronous behaviour. This class of systems belongs to the two dimensional mixed Li\'enard- type equations and is obtained by generalizing the…
In this work we present a general strategy for constructing multidimensional Riemann solvers with a single intermediate state, with particular attention paid to detailing the two-dimensional Riemann solver. This is accomplished by…
In this paper, we establish the non-uniqueness of solutions to the ideal magnetohydrodynamics equations in any dimension greater than three by proving the existence of infinitely many compactly supported weak solutions. In particular, these…
We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the…
We consider a variant of the Seiberg-Witten equations for multiple-spinors. The moduli space of solutions to our generalized Seiberg-Witten equations in the setting of K\"ahler surfaces has a direct relation with ASD connections of…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…
Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method, which is applicable more generally to other nonlinear PDEs, involves an ansatz technique to solve a first-order PDE system…
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of…
Many interesting terrestrial and astrophysical scenarios involving magnetic fields can be approached in axial geometry. Even though the Lagrangian smoothed particle hydrodynamics (SPH) technique has been successfully extended to handle…