Related papers: Natural Higher-Derivatives Generalization for the …
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed.…
We develop an operator approach to the integration of linear differential equations based on intertwining relations between differential operators. Conditions for the existence of intertwining operators are obtained, and it is shown that,…
The relativistic Klein-Gordon system is studied as an illustration of Quantum Mechanics using non-Hermitian operators as observables. A version of the model is considered containing a generic coordinate- and energy-dependent…
We establish a priori Lipschitz estimates for unbounded solutions of second-order Hamilton-Jacobi equations in R^N in presence of an Ornstein-Uhlenbeck drift. We generalize the results obtained by Fujita, Ishii \& Loreti (2006) in several…
A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…
We provide a rigorous derivation of the Landau-Pekar equations from the Fr\"ohlich Hamiltonian in the mean-field limit using Wigner measure techniques. On the classical side, we extend the global well-posedness results up to $L^2 \oplus…
The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component…
It is pointed out that the solutions of the Klein-Gordon and the Dirac equation derived in the paper addressed in this Comment (and many more solutions) may be obtained from generating functions.
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
In this work we introduce two different generalizations of the Fokker-Planck equation in (1+1) dimensions by replacing the spatial derivatives in terms of generalized Dunkl-type derivatives involving reflection operators. As applications of…
We show that the momentum, the density, and the electromagnetic field associated with the massive KleinGordon-Maxwell equations converge in the semi-classical limit towards their respective equivalents associated with the relativistic…
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive…
We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the…
The purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude group reduced ordinary differential equations…
Building on the hyperboloidal foliation approach of Lefloch and Ma, we extend Klainerman's physical-space approach to dispersive estimates to recover the frequency-restricted $L^1$--$L^\infty$ dispersive estimates for Klein-Gordon…
We propose a natural gradient term for a class of second-order partial differential equations of the form \begin{equation}\nonumber M(x,Du,D^2u)+g(u)N(x,Du, D^2u)+f(x,u)=0 \;\;\mbox{in}\;\; \Omega, \end{equation} where…
We consider the problem of solvability of linear differential equations over a differential field~$K$. We introduce a class of special differential field extensions, which widely generalizes the classical class of extensions of differential…
In this paper, we obtain an analogue of the Serre derivation acting on the product of spaces of Drinfeld modular forms which generalizes the differential operator introduced by Gekeler in the rank two case. We further introduce a finitely…
In this paper, we consider the Dirichlet problem for a new class of augmented Hessian equations. Under sharp assumptions that the matrix function in the augmented Hessian is regular and there exists a smooth subsolution, we establish global…
Using the elementary axioms of special relativity and quantum mechanics we construct a wave equation which generalizes the Schrodinger equation. We also solve the general second and some higher order differential equations.