This is the second volume of the new series “Mathematics and its Applications” published by the Union of Bulgarian Mathematicians∗ Petar Popivanov, the author of the book, is a well known expert in the theory of partial differential equations (PDE), who has published several books and over 120 research articles. Since 1969 he works at the Institute of Mathematics and Informatics of the Bulgaria...

in this paper, optimum location of power system stabilizers in order to damp inter-area oscillations has been investigated by using modal series method. nonlinear effects grow in dynamical behaviors of heavily loaded stressed power systems significantly. hence linear based methods and techniques no longer present clear and exact response of the systems. in this article by defining new nonlinear...

in this paper coupled nonlinear equations of motion of a suspended cable with time dependent tension and velocity are derived by using hamilton’s principal. a modal analysis for a stationary sagged cable is initially carried out in order to identify the dynamic system. the natural solution is directed to compute the natural frequencies and mode shapes of the free vibration of a suspended cable....

background and purpose: multiple sclerosis (ms) is a chronic disease that gives rise to a number of unpleasant symptoms that can be difficult to manage by conventional means. there are some aspects of ms-related disability which can be improved by using deep brain stimulation (dbs); particularly movement disorders, such as tremor. the research aim is to study the effect of dbs on ms tremor with...

– We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and...

Autonomous vehicles with nonlinear dynamics need to have a planned reference trajectory and a feedback controller to accomplish the task of traveling from a launch point to a goal point. Traditionally the planning stage has either been done from a purely geometrical point of view without regarding the dynamic constraints of the system, or by time-consuming numerical optimization including the d...

Abstract. We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We remark that the conditions we consider can be easily verified. Moreover we show that multiplicity of solitons of the same charge is guaranteed by t...

We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear Dirichletto-Neumann map. The result is constructive and local, and gives a method for determining the coefficient at a boundary point from measurements in a small n...

A statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrödinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can st...