We study the issue of stability of static soliton-like solutions in some non-linear field theories which allow for knotted field configurations. Concretely, we investigate the AFZ model, based on a La-grangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with differen...

We explore the space of solutions of the classical equations of motion in the Euclidean electroweak theory. We sketch a topological prescription that finds known solutions and indicates the existence of novel ones. All spatially–varying, time– independent solutions are unstable. However, if we consider quantum fluctuations around static classical configurations, it may be possible to find stabl...

The noncommutative soliton is characterized by the use of the projection operators in non-commutative space. By using the close relation with the K-theory of C∗-algebra, we consider the variations of projection operators along the commutative directions and identify their topological charges. When applied to the string theory, it gives the modification of the brane charges due to tachyon backgr...

The O(3) Skyrme system in two space dimensions admits topological soliton solutions. This paper studies the transition between the high-density crystalline phase of such solitons and the low-density phase where there are multi-Skyrmions localized in space. The details depend crucially on the choice of the potential function. Two such choices are investigated: in the first system, multi-Skyrmion...

A periodically inhomogeneous Schrödinger equation is considered. The inhomogeneity is reflected through a non-uniform coefficient of the linear and non-linear term in the equation. Due to the periodic inhomogeneity of the linear term, the system may admit spectral bands. When the oscillation frequency of a localized solution resides in one of the finite band gaps, the solution is a gap soliton,...

In this letter, we established a traveling wave solution by using cosine function algorithm for Gardnerequation and (2+1)-dimensional breaking soliton system. The cosine method is used to obtain theexact solution.

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...