Related papers: Isotropic extension of first-order wave equations
In this article we classify vessels producing solutions of some completely integrable PDEs, presenting a \textit{unified} approach for them. The classification includes such important examples as Korteweg-de Vries (KdV) and evolutionary Non…
The inverse scattering transform allows explicit construction of solutions to many physically significant nonlinear wave equations. Notably, this method can be extended to fractional nonlinear evolution equations characterized by anomalous…
We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI0-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an…
In this work, we investigate non-classical wavetrain formations, and particularly dispersive shock waves (DSWs), or undular bores, in systems exhibiting non-convex dispersion. Our prototypical model, which arises in shallow water wave…
In the present work, we study the dynamical evolution of an homogeneous and anisotropic KS cosmological model, considering general relativity as the gravitational theory, such that there are three different perfect fluids in the matter…
For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction…
Context. Turbulent convection models in nonlinear radial stellar pulsation models rely on an extra equation for turbulent kinetic energy and fail to adequately explain mode-selection problems. Since multidimensional calculations are…
The Korteweg-de Vries equation u_t+uu_x+u_{xxx}=0 is PT symmetric (invariant under space-time reflection). Therefore, it can be generalized and extended into the complex domain in such a way as to preserve the PT symmetry. The result is the…
The core focus of this research work is to obtain invariant solutions and conservation laws of the (3+1)-dimensional ZK equation, a higher-dimensional generalization of the Korteweg--de Vries (KdV) equation, which describes the phenomenon…
We study solutions to the linear wave equation on the cosmological region of Schwarzschild-de Sitter spacetimes. We show that all sufficiently regular finite-energy solutions to the linear equation possess a particular finite-order…
We consider scalar conservation laws with nonlocal diffusion of Riesz-Feller type such as the fractal Burgers equation. The existence of traveling wave solutions with monotone decreasing profile has been established recently (in special…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
This article investigates uniform well-posedness and inviscid limit behavior for the periodic Korteweg-de Vries-Burgers (KdV-B) and modified Korteweg-de Vries-Burgers (mKdV-B) equations: \[ \partial_t u + \partial_x^3 u - \varepsilon…
We generalize the derivation of viscous anisotropic hydrodynamics from kinetic theory to allow for non-zero particle masses. The macroscopic theory is obtained by taking moments of the Boltzmann equation after expanding the distribution…
We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a…
Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to…
In the minimal formulation of gravity with Lifshitz-type anisotropic scaling, the gauge symmetries of the system are foliation-preserving diffeomorphisms of spacetime. Consequently, compared to general relativity, the spectrum contains an…
We present a framework to describe completely general first-order perturbations of static, spatially compact, and locally rotationally symmetric class II spacetimes within the theory of general relativity. The perturbation variables are by…
The Korteweg-de Vries (KdV) equation is of fundamental importance in a wide range of subjects with generalization to multi-component systems relevant for multi-species fluids and cold atomic mixtures. We present a general framework in which…
In this paper, we study the hydrodynamic limits of both the Landau equation and the Vlasov-Maxwell-Landau system in the whole space. Our main purpose is two-fold: the first one is to give a rigorous derivation of the compressible Euler…