Self-Induced Transparency Solitons and Dissipative Solitons in Microwave Electronic Systems

Radiophysics and Quantum Electronics - Solitons are a well-studied subject in many domains of nonlinear physics, including hydrodynamics, plasma physics, optics, etc. However, it has been...     

Theory of active-passive mode-locking of solid-state lasers using a nonlinear mirror

The theory of active-passive mode-locked solid-state lasers is developed where the passive mode-locking is achieved by a nonlinear mirror. Steady-state cw numerical solutions are analyzed in detail for the case of a Nd: YAG laser. The steady-state pulse duration can be reduced by an order of magnitude as compared to the pure active mode-locking regime.On leave from Department of Quantum Electronics, Faculty of Physics, University of Sofia, BG-1126 Sofia, Bulgaria     

Application of Exp-function method to Symmetric Regularized Long Wave (SRLW) equation

In this Letter, the Exp-function method with the aid of Maple is used to obtain generalized soliton solution and periodic solution with some free parameters for the Symmetric Regularized Long Wave (SRLW) equation. Suitable choice of parameters in the generalized solution leads to Darwish's solution [A.A. Darwish, A. Ramady, Chaos Solitons Fractals 33 (4) (2007) 1263]. The result shows that Exp-function method is a powerful mathematical tool for solving nonlinear equations arising in mathematical physics.     

Negative feedback using a nonlinear mirror for the generation of a long train of short light pulses

A nonlinear mirror is used to provide a passive negative feedback in an actively mode-locked pulsed Nd:YAG laser. Trains of 250 ps pulses with a total length of up to 50 microseconds were generated. The train duration is limited only by the flashlamp pump pulse length.On leave from Department of Physics, University of Sofia, BG-1126 Sofia, Bulgaria     

A mirror with an intensity-dependent reflection coefficient

A device exhibiting a power-dependent reflection coefficient with fast time response and no frequency shift is proposed and analysed. It utilizes a combination of a nonlinear crystal for second harmonic generation and a dichroic mirror with high reflectivity for the second harmonic and partial transmission for the fundamental wavelenth. This device has been successfully used in a preliminary experiment to modelock a Nd:YAG laser.Department of Physics, Sofia University, BG-1126, Sofia, Bulgaria.     

量子物理学百年回顾

简述了量子物理学诞生的背景。它的诞生,打开了人们认识微观物质世界运动规律的大门。物质属性及其微观结构问题,只有在量子物理的基础上才在原则上得以解决．量子力学提供了所有现代科学的基础支柱。在过去一百年中,量子物理不仅对于说明众多自然现象取得了无与伦比的成功,它还引发了大量的技术应用。由于量子物理学的基本概念与人们日常生活经验如此不同,诞生伊始至今,对于量子力学原理的诠释存在持续不断的争论。量子理论以前所未有的深度改变了人们的世界观。     

Introductive Backgrounds to Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems

Introductive backgrounds to a new mathematical physics discipline—Quantum Mathematics—are discussed and analyzed both from historical and from analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered. The Authors devote their article to their Friend and Teacher academician Prof. Anatoliy M. Samoilenko on occasion of his 70 years-Birthday with great compliments and gratitude to his brilliant talent and impressive impact to modern theory of nonlinear dynamical systems of mathematical physics and nonlinear analysis     

Geometrical interpretation of Benenti systems

We show that the following two separately developed theories, the theory of Benenti systems in mathematical physics and the theory of projectively equivalent metrics in classical differential geometry, study essentially the same object. Combining methods and results from these two theories, one can prove the commutative integrability of projectively equivalent pseudo-Riemannian metrics and construct infinitely many new Hamiltonian systems, integrable in the classical and in the quantum sense.     

Glafka-2004: Categorical Quantum Gravity

A synopsis-cum-update of work in the past half-decade or so on applying the algebraico-categorical concepts, technology and general philosophy of Abstract Differential Geometry (ADG) to various issues in current classical and quantum gravity research is presented. The exposition is mainly discursive, with conceptual, interpretational and philosophical matters emphasized throughout, while their formal technical-mathematical underpinnings have been left to the original papers. The general position is assumed that Quantum Gravity is in need of a new mathematical, novel physical concepts and principles introducing, framework in which old and current problems can be reformulated, readdressed and potentially retackled afresh. It is suggested that ADG can qualify as such a theoretical framework.Paper version of a talk given at the Glafka–2004: Iconoclastic Approaches to Quantum Gravity international theoretical physics conference, held in Athens, Greece (summer 2004).     

Soliton-like solutions for the nonlinear schr?dinger equation with variable quadratic hamiltonians

We construct one-soliton solutions for the nonlinear Schr¨odinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of the complete (super) integrability of generalized harmonic oscillators. The soliton-wave evolution in external fields with variable quadratic potentials is totally determined by the linear problem, like motion of a classical particle with acceleration, and the (self-similar) soliton shape is due to a subtle balance between the linear Hamiltonian (dispersion and potential) and nonlinearity in the Schr¨odinger equation by the standards of soliton theory. Most linear (hypergeometric, Bessel) and a few nonlinear (Jacobian elliptic, second Painlev′e transcendental) classical special functions of mathematical physics are linked together through these solutions, thus providing a variety of nonlinear integrable cases. Examples include bright and dark solitons and Jacobi elliptic and second Painlev′e transcendental solutions for several variable Hamiltonians that are important for research in nonlinear optics, plasma physics, and Bose–Einstein condensation. The Feshbach-resonance matter-wave-soliton management is briefly discussed from this new perspective.     

Solitons in condensed matter: A paradigm

For this new journal dealing with nonlinear phenomena we review the setting of several important current problems in the physics of condensed matter (solids, liquids). We show how the concepts embodied in the mathematical analysis of solitons provide systematic new insight (i.e., a paradigm) into a central question: what are the important physical configurations in nonlinear condensed systems? Following these general issues we summarize the analysis of the dynamics and equilibrium thermodynamics (i.e., statistical mechanics) of non-linear one-dimensional model systems, and we indicate how the solitonic configurational phenomenology provides a basis for dynamic effects which are seen both experimentally and in molecular dynamics computer simulations. Many problems in condensed matter differ from the more familiar nonlinear mechanical or hydrodynamic applications in that finite temperature thermal fluctuations must be considered along with systematic dynamics.     

Simulations: A tool for studying quantum condensed matter systems

Quantum Monte Carlo techniques provide a new method for studying the properties of condensed matter systems. A review of this approach and the type of information which it can provide is given. Talk presented at the Frontiers of Monte Carlo Meeting, Los Alamos National Laboratory, September, 1985.     

Local behavior of solutions of some elliptic equations

We study the local behavior of solutions of some nonlinear elliptic equations. These equations are of interest in differential geometry and mathematical physics.     

The effective geometry Monte Carlo algorithm: Applications to molecular communication

In this work, we address the systematic biases and random errors stemming from finite step sizes encountered in diffusion simulations. We introduce the Effective Geometry Monte Carlo (EG-MC) simulation algorithm which modifies the geometry of the receiver. We motivate our approach in a 1D toy model and then apply our findings to a spherical absorbing receiver in a 3D unbounded environment. We show that with minimal computational cost the impulse response of this receiver can be precisely simulated using EG-MC. Afterwards, we demonstrate the accuracy of our simulations and give tight constraints on the single free parameter in EG-MC. Finally, we comment on the range of applicability of our results. While we present the EG-MC algorithm for the specific case of molecular diffusion, we believe that analogous methods with effective geometry manipulations can be utilized to approach a variety of problems in other branches of physics such as condensed matter physics and cosmological large scale structure simulations.     

一类高阶非线性波方程的李群分析、最优系统、精确解和守恒律

本文运用李群分析的方法研究了一类高阶非线性波方程,得到了五阶非线性波方程的对称以及方程的最优系统,进而运用幂级数的方法,求得了方程的精确幂级数解.最后,给出了五阶非线性波方程的一些守恒律.     

Analysis of the dispersion relations of nonlinear slab-guided waves

The dispersion relations of TE-polarized nonlinear guided waves (NGW) were investigated in detail. These waves travel along a dielectric slab embedded between two different nonlinear media. A simple relation between the effective nonlinear dielectric constants was established. All dispersion curves exhibit a particular transition point, where one evanescent field maximum changes from a virtual into a real one, and vice versa. Depending on the type of the remaining invariant evanescent field maximum, all NGW's split into two families. The lowest-order membres of every family play a particular role. The power flux supported by a NGW is derived, too.Preliminary results were presented at the XVI^th European Congress of Molecular Spectroscopy, Sofia, Bulgaria (1983)     

Exact traveling wave solutions of an autonomous system via the enhanced (G′/G)-expansion method

Mathematical modeling of many autonomous physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear evolution equations plays a significant role in the study of nonlinear physical phenomena. In this article, the enhanced (G′/G)-expansion method has been applied for finding the exact traveling wave solutions of longitudinal wave motion equation in a nonlinear magneto-electro-elastic circular rod. Each of the obtained solutions contains an explicit function of the variables in the considered equations. It has been shown that the applied method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering fields.     

Neutrino interactions in dense stellar matter

Weak-interaction rates play an important role in the birth of neutron stars in core collapse supernova and their subsequent thermal evolution. In this paper, I highlight the role of strong interactions and phase transitions in calculations of neutrino scattering and emission rates in dense stellar matter.Received: 1 November 2002, Published online: 15 July 2003PACS: 13.15.+g Neutrino interactions - 13.20.-v Leptonic and semileptonic decays of mesons - 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environments - 26.60.+c Nuclear matter aspects of neutron starsPresent address: Los Alamos National Laboratory, P.O. Box 1663, MS B283, Los Alamos, NM 87545, USA     

On a class of exactly soluble statistical mechanical models with nonpolynomial interactions

The approximating Hamiltonian method of N. N. Bogolubov, Jr. is generalized to models with nonpolynomial intensive-observable interactions. The original Hamiltonian is proved to be thermodynamically equivalent to one linear in the intensive-observable trial Hamiltonian. We show that the exact expression for the free energy density in the thermodynamic limit can be obtained from a min-max principle for the system with trial Hamiltonian.On leave of absence from Institute for Nuclear Research and Nuclear Energetics, Bulgarian Academy of Sciences, Sofia, Bulgaria.On leave of absence from Institute for Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria.