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Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex…
The exact solutions of the first order differential equation with delay are derived. The equation has been introduced as a model of traffic flow. The solution describes the traveling cluster of jam, which is characterized by Jacobi's…
This paper investigates a new class of equations called measure functional differential equations with state-dependent delays. We establish the existence and uniqueness of solutions and present a discussion concerning the appropriate phase…
This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…
For an open quantum system described by the Lindblad equation, full characterization of its dynamics typically needs the knowledge of the Liouvillian spectrum and correlation functions. Solving the Liouvillian spectrum and correlation…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
We present a family of exact analytic solutions for non-linear quantum dynamics of a two-level system (TLS) subject to a periodic-in-time external field. In constructing the exactly solvable models, we use a "reverse engineering" approach…
In this paper we study the phase of self-similar solutions to general Nonlinear Schr\"odinger equations. From this analysis we gain insight on the dynamics of nontrivial solutions and a deeper understanding of the way collective coordinate…
The linear nonhomogeneous fractional difference system with constant coefficients is introduced. An explicit solution to the system is acquired by proposing a newly discrete retarded perturbation of the nabla Mittag-Leffer-type function…
We establish a rigorous mathematical framework connecting graphene nanoribbon quantum sensing to the Lambert W function through the finite square well (FSW) analogy. The Lambert W function, defined as the inverse of $f(W) = We^W$, provides…
The Lambert W function gives the solutions of a simple exponential polynomial. The generalized Lambert W function was defined by Mez\"{o} and Baricz, and has found applications in delay differential equations and physics. In this article we…
In this paper, we investigate the delay differential equations of Malmquist type of form \begin{equation*} w(z+1)-w(z-1)+a(z)\frac{w'(z)}{w(z)}=R(z, w(z)),~~~~~~~~~~~~~~(*) \end{equation*} where $R(z, w(z))$ is an irreducible rational…
The paper derived differential equations which solve the problem of restoration the motion parameters for a rigid reference frame from the known proper acceleration and angular velocity of its origin as functions of proper time. These…
The applications of the recent results obtained in the theory of generalized Lambert functions, to the mean field theory of ferromagnetism are presented. As a consequence, all the predictions of the Weiss theory of ferromagnetism can be…
We report a new analytical method for exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension…
In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
This paper delves into a novel class of functions defined on an invariant under translation time scale T, known as (w, c)-periodic functions. This class encompasses various types of functions, such as periodic, anti-periodic, Bloch, and…
Rectangular matrix solutions of the defocusing nonlinear Schr\"odinger equation (dNLS) are considered on a semi-strip. Evolution of the corresponding Weyl function is described in terms of the initial-boundary conditions. Then initial…