Related papers: Stability Analysis of Classical String Solutions a…
{\bf Exact} solutions of the string equations of motion and constraints are {\bf systematically} constructed in de Sitter spacetime using the dressing method of soliton theory. The string dynamics in de Sitter spacetime is integrable due to…
We apply the dressing method on the Non Linear Sigma Model (NLSM), which describes the propagation of strings on $\mathbb{R}\times \mathrm{S}^2$, for an arbitrary seed. We obtain a formal solution of the corresponding auxiliary system,…
We obtain classical string solutions on RxS^2 by applying the dressing method on string solutions with elliptic Pohlmeyer counterparts. This is realized through the use of the simplest possible dressing factor, which possesses just a pair…
We analyse several physical aspects of the dressed elliptic strings propagating on $\mathbb{R} \times \mathrm{S}^2$ and of their counterparts in the Pohlmeyer reduced theory, i.e. the sine-Gordon equation. The solutions are divided into two…
A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…
In this paper, we develop the dressing method to study the exact solutions for the vector sine-Gordon equation. The explicit formulas for one kink and one breather are derived. The method can be used to construct multi-soliton solutions.…
We apply the dressing method to a string solution given by a static string wrapped around the equator of a three-sphere and find that the result is the single spike solution recently discussed in the literature. Further application of the…
This paper deals with stability of classical Runge-Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [12] and used in [13] for the time integration of nonlinear evolution PDEs, the…
Critical dressing, the simultaneous dressing of two spin species to the same effective Larmor frequency, is a technique that can, in principle, improve the sensitivity to small frequency shifts. The benefits of spin dressing and thus…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
We use integrability to construct the general classical splitting string solution on R x S^3. Namely, given any incoming string solution satisfying a necessary self-intersection property at some given instant in time, we use the…
The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…
This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string…
Higher-order solitons, as well as simple $N$-soliton solutions, of the Gerdjikov-Ivanov equation are derived by the dressing method based on the technique of regularization. By the dressing transformation for the eigenfunction associated…
We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…
Planning accurate manipulation for deformable objects requires prediction of their state. The prediction is often complicated by a loss of stability that may result in collapse of the deformable object. In this work, stability of a fabric…
It is argued that the (NS-sector) superstring field equations are integrable, i.e. their solutions are obtainable from linear equations. We adapt the 25-year-old solution-generating "dressing" method and reduce the construction of…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
Nowadays we are witnessing a transformation of the business processes towards a more computation driven approach. The ever increasing usage of Machine Learning techniques is the clearest example of such trend. This sort of revolution is…