Search results for "Exact differential equation"

Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

2020

The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed …

Constrained control of a nonlinear two point boundary value problem, I

1994

In this paper we consider an optimal control problem for a nonlinear second order ordinary differential equation with integral constraints. A necessary optimality condition in form of the Pontryagin minimum principle is derived. The proof is based on McShane-variations of the optimal control, a thorough study of their behaviour in dependence of some denning parameters, a generalized Green formula for second order ordinary differential equations with measurable coefficients and certain tools of convex analysis.

Exact solution of generalized Tavis - Cummings models in quantum optics

1996

Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations M. Either a Kerr-type nonlinearity or a Stark-shift term can be included in the model, and it is shown that these two cases can be mapped from one to the other. The method of solution provides a general framework within which many related problems can similarly be solved. Explicit formulae are given for the Rabi splitting of the models for some N and M, on- and off-resonance. It is also shown that the solution of the pure Tavis - Cummings model can be reduced to solving a homogen…

Early Vision and Soft Computing

2002

The term soft-computing has been introduced by Zadeh in 1994. Soft-computing provides an appropriate paradigm to program malleable and smooth concepts. For example, it can be used to introduce flexibility in artificial systems and possibly to improve their Intelligent Quotient. Aim of this paper is to describe the applicability of soft-computing to early vision problems. The good performance of this approach is claimed by the fact that digital images are examples of fuzzy entities, where geometry of shapes are not always describable by exact equations and their approximation can be very complex.

Exact spherically-symmetric inhomogeneous model withnperfect fluids

2011

We present the exact equations governing the dynamics of a spherically-symmetric inhomogeneous model with n decoupled and non-comoving perfect fluids. Thanks to the use of physically meaningful quantities we write the set of 3+2n equations in a concise and transparent way. The n perfect fluids can have general equations of state, thus making the model extremely flexible to study a large variety of cosmological and astrophysical problems. As applications we consider a model sourced by two non-comoving dust components and a cosmological constant, and a model featuring dust and a dark energy component with negligible speed of sound.

Nonlinear mechanics of DNA doule strand: existence of the compact-envelope bright solitary wave

2013

We study the nonlinear dynamics of a homogeneous DNA chain which is based on site-dependent finite stacking and pairing enthalpies. We introduce an extended nonlinear Schrödinger equation describing the dynamics of modulated wave in DNA model. We obtain envelope bright solitary waves with compact support as a solution. Analytical criteria of existence of this solution are derived. The stability of bright compactons is confirmed by numerical simulations of the exact equations of the lattice. The impact of the finite stacking energy is investigated and we show that some of these compact bright solitary waves are robust, while others decompose very quickly depending on the finite stacking para…

On a singular boundary value problem for a second order ordinary differential equation

2000

A FAMILY OF THE SPIRAL SOLUTIONS OF THE NONLINEAR KLEIN‐GORDON EQUATION

1998

A family of the functions, intended for a construction the exact travelling wave solutions of nonlinear partial differential equations, is given. Exact solutions of the Klein‐Gordon equation with a special potential are obtained. The behavior of complex and hypercomplex solutions of the second order is presented. First Published Online: 14 Oct 2010

Compact-envelope bright solitary wave in a DNA double strand

2012

International audience; We study the nonlinear dynamics of a homogeneous DNA chain which is based on site-dependent finite stacking and pairing enthalpies. We introduce an extended nonlinear Schroedinger equation describing the dynamics of modulated waves in DNA model. We obtain envelope bright solitary waves with compact support as a solution. Analytical criteria of existence and stability of this solution are derived. The stability of bright compactons is confirmed by numerical simulations of the exact equations of the lattice. The impact of the fi nite stacking energy is investigated and we show that some of these compact bright solitary waves are very robust, while others decompose quic…

Discreteness effects on a sine-Gordon breather

1991

We employ collective-variable theory to describe the dynamics of a breather excitation in its center-of-mass frame in continuous and discrete systems of one spatial dimension. The exact equations of motion for the collective variable and coupled phonon field are derived for any system which supports breatherlike excitations that have even spatial parity where the collective variable represents half the distance between the breather subkinks. We then specialize the theory to the sine-Gordon (SG) case. For the continuum SG system we derive the exact effective potential in terms of the collective variable and discuss the relativistic effects on the breather subkinks which are quite different t…