相关论文: Effective Methods for Norm-Form Equations
Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…
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…
The objective of this study is to ascertain the existence and forms of the finite order meromorphic and entire functions of several complex variables satisfying some certain Fermat-type partial differential-difference equations by…
In 1993, a proof was published, within ``Classical and Quantum Gravity,'' that there are no regular solutions to the {\it linearized} version of the twisting, type-N, vacuum solutions of the Einstein field equations. While this proof is…
We study universal electromagnetic (test) fields, i.e., p-forms fields F that solve simultaneously (virtually) any generalized electrodynamics (containing arbitrary powers and derivatives of F in the field equations) in n spacetime…
In this work we extend the range of applicability of a method recently introduced where coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. Some general consequences of the present…
Naz and Chaudhry [3] established multiple closed-form solutions for the basic Lucas-Uzawa model. According to Boucekkine and Ruiz-Tamarit [1] and Chilarescu [2] unique closed-form solutions exist for the basic Lucas-Uzawa model. We equate…
We give simple necessary and sufficient conditions for the $\frac{\partial}{\partial t}$-transcendence of the solutions to a parameterized second order linear differential equation of the form \frac{\partial^2 Y}{\partial x^2} - p…
We address the six vertex model on a random lattice, which in combinatorial terms corresponds to the enumeration of weighted 4-valent planar maps equipped with an Eulerian orientation. This problem was exactly, albeit non-rigorously solved…
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
Let $V\subset \mathbb{F}_q^d$ be a \textit{regular} variety, $k\ge 3$ is an integer and $A\subseteq V$. Covert, Koh, and Pi (2017) proved the following generalization of the Erd\H{o}s-Falconer distance problem: If $|A|\gg…
This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…
We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory allowing to handle generalized integrals weighted by an exponential coefficient. The results are applied to the fractional…
The Thomas - Fermi equation describing the screening of the Coulomb potential inside heavy neutral atoms is reconsidered. An accurate representation for its numerical solution was obtained by means of the variational principle. The proposed…
We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly via the functional Bethe ansatz method. For each case, we give closed-form solutions…
In classical continuum theory, Volterra's principle [1, 2] is a long-known method to solve linear rheological (viscoelastic) problems derived from the corresponding elastic ones. Here, we introduce and present another approach that is…
We present a technique for derivation of a priori bounds for Gevrey-Sobolev norms of space-periodic three-dimensional solutions to evolutionary partial differential equations of hydrodynamic type. It involves a transformation of the flow…
In this paper we establish a necessary and sufficient condition for solving a general class of fully nonlinear elliptic equations on compact almost Hermitian manifolds, extending a recent work of Guo-Song. As applications, we determine the…
It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a…
In the paper, a Newton-type method for the solution of generalized equations (GEs) is derived, where the linearization concerns both the single-valued and the multi-valued part of the considered GE. The method is based on the new notion of…