In this paper we study a one-dimensional dynamic model of dry friction with slip velocity dependent coefficient. In many cases, this model has more than one solution. We introduce a perturbed friction condition which allows us to regain the uniqueness of the solution. We show that the perturbed problem's solutions pointwise converge to a particular solution of the initial problem when the pertu...

The Traveling Salesman Problem with Pickup and Delivery (PDTSP) is considered. Seven perturbation heuristics are applied to instances ranging from 51 to 443 vertices. The main point of perturbation heuristics is to help a local search process to move away from a local optimum. The seven heuristics fall into three categories: Instance Perturbation (IP), Algorithmic Perturbation (AP), and Solutio...

In this paper a nonlinear matrix equation is considered. Perturbation estimations for the maximal solution of the considered equation are obtained. The results are illustrated by the use of numerical examples. MSC: 65F10; 15A24 keywords: nonlinear matrix equation, perturbation estimates

A new type of multi-soliton solution to the ultradiscrete Toda equation is proposed. The solution can be transformed into another expression of solution in a perturbation form. A direct proof of the solution is also given.

Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The perturbation is represented by finite collections of harmonics. The frequencies of the perturbation vary slowly and pass through the resonant values consecutively. The resonances lead to the sequence of the wave packets with the different fast oscillated carriers. Full asymptotic description o...