Related papers: The Characteristic Functions and Their Typical Val…
Solutions to nonlinear integro-differential systems are regular outside a negligible closed subset whose Hausdorff dimension can be explicitly bounded from above. This subset can be characterized using quantitative, universal energy…
Nonlinear spin dynamics are essential in exploring nonequilibrium quantum phenomena and have broad applications in precision measurement. Among these systems, the combination of a bias magnetic field and feedback mechanisms can induce…
We study the behaviour near a boundary point a of any positive solution of a nonlinear elliptic equations with forcing term which vanishes on the boundary except at a. Our results are based upon a priori estimates for solutions and…
Model-independent identities and inequalities relating the various spin observables of a reaction are reviewed in a unified formalism, together with their implications for dynamical models, their physical interpretation, and the quantum…
We derive the node structure of the radial functions which are solutions of the Dirac equation with scalar $S$ and vector $V$ confining central potentials, in the conditions of exact spin or pseudospin symmetry, i.e., when one has $V=\pm…
Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
A model "remarkable" fin equation is singled out from a class of nonlinear (1+1)-dimensional fin equations. For this equation a number of exact solutions are constructed by means of using both classical Lie algorithm and different modern…
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
The present work proposes a discussion on the self-energy of charged particles in the framework of nonlinear electrodynamics. We seek magnet- ically stable solutions generated by purely electric charges whose electric and magnetic fields…
It is shown that the nonselfadjoint (and non-normal) linear ordinary differential operators of a certain class are spectral operators of scalar type in the sense of Dunford and Bade. Operators of this kind appear in physical problems such…
In this paper, we study the nonlinear Schr\"{o}dinger equation with non-symmetric electromagnetic fields $$\Big(\frac{\nabla}{i}-A_{\epsilon} x)\Big)^2 u+V_{\epsilon}(x)u=f(u),\ u\in H^1 (\mathbb{R}^N,\mathbb{C}), $$ where…
Unlike the simplest (Hooke's law spring) oscillator, where the restoring force is in magnitude proportional to the displacement; the yo-yo oscillator has a constant force-magnitude. In other words, its potential energy function is linear,…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the…
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…
The paper considers the general form of self-adjoint boundary value problems for momentum operators with nonlocal potentials. We give an analysis of the eigenvalue distribution as zeros of the characteristic functions, for which their…
In this work we classify all radial non-radiative solutions to the 5D nonlinear wave equations with a wide range of energy critical nonlinearity. We show that such a solution always comes with two characteristic numbers. These…
The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…