Related papers: Oscillons in a perturbed signum-Gordon model
The sine-Gordon model in the presence of dynamical integrable defects is investigated. This is an application of the algebraic formulation introduced for integrable defects in earlier works. The quantities in involution as well as the…
We adopt a variational technique to study the dynamics of perturbed dissipative solitons, whose evolution is governed by a Ginzburg--Landau equation (GLE). As a specific example of such solitons, we consider a silicon-based active waveguide…
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states together with their reflection factors by closing the boundary bootstrap and…
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint…
We propose a new system identification method, called Sign-Perturbed Sums (SPS), for constructing non-asymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not…
We derive a sufficient condition guaranteeing that a singularly perturbed linear time-varying system is strongly monotone with respect to a matrix cone $C$ of rank $k$. This implies that the singularly perturbed system inherits the…
It is known that including vector mesons stabilizes the size of a Skyrmion without the need for a Skyrme term. This paper provides the first results for static multi-Skyrmions in such a theory. The rational map ansatz is used to investigate…
This article deals with the multidimensional Borg-Levinson theorem for perturbed bi-harmonic operator. More precisely, in a bounded smooth domain of $\R^n$, with $n \geq 2$, we prove the stability of the first and zero order coefficients of…
We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations…
We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…
In this work, we introduce two spatio-temporal colored bounded noises, based on the zero-dimensional Cai-Lin and Tsallis-Borland noises. We then study and characterize the dependence of the defined bounded noises on both a temporal…
Oscillons, extremely long-living localized oscillations of a scalar field, are studied in theories with quartic and sine-Gordon potentials in two spatial dimensions. We present qualitative results concentrating largely on a study in…
We examine spherical p-branes in AdS_m x S^n, that wrap an S^p in either AdS_m (p=m-2) or S^n (p=n-2). We first construct a two-spin giant solution expanding in S^n and has spins both in AdS_m and S^n. For (m,n)={(5,5),(4,7),(7,4)}, it is…
The forced time harmonic response of a spatiotemporally-modulated elastic beam of finite length with light damping is derived using a novel Green's function approach. Closed-form solutions are found that highlight unique mode coupling…
Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longer present at the chosen parameter value. For bifurcating…
The baby Skyrme model is a well-known nonlinear field theory supporting topological solitons in two space dimensions. In the limit where the term quadratic in derivatives (the "sigma model term") vanishes some additional structure emerges.…
Topologically stable non-Abelian sine-Gordon solitons have been found recently in the $U(N)$ chiral Lagrangian and a $U(N)$ gauge theory with two $N$ by $N$ complex scalar fields coupled to each other. We construct the effective theory on a…
A dynamical system of equations describing parametric sound generation (PSG) in a dispersive large aspect ratio resonator is derived. The model generalizes previously proposed descriptions of PSG by including diffraction effects, and is…
We consider the perturbed sine-Gordon equation $\theta_{tt}-\theta_{xx}+\sin \theta= \varepsilon^2 f(\varepsilon x)$, where the external perturbation $\varepsilon^2 f(\varepsilon x)$ corresponds to a small, slowly varying electric field. We…
We perform some simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime. We reported the accurate numerical results of the equation with the structure-preserving scheme (SPS) in an earlier publication (Tsuchiya and…