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A family of solitary waves is constructed in Frenkel-Kontorova model and its continuum and quasi-continuum approximations. Each solitary waves is characterised by the number of local maxima in its profile and a relation between external…
Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet and which preserves this localization in time. A soliton is a solitary wave which exhibits some strong form of stability so that…
We study the properties of a relativistic model with logarithmic nonlinearity. We show that such model allows two types of solutions: topologically trivial (gaussons) and topologically non-trivial (kinks), depending on a sign of the…
We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $\alpha+1$ with $\frac43<\alpha<3$, we employ…
We show that the leading semiclassical behavior of soliton form factors at arbitrary momentum transfer is controlled by solutions to a new wave-like integro-differential equation that describes solitons undergoing acceleration. We work in…
The light-cone gauge approach to $T\overline{T}$ deformed models is used to derive the $T\overline{T}$ deformed matrix nonlinear Schr\"odinger equation, the Landau--Lifshitz equation, and the Gardner equation. Properties of one-soliton…
In this article, we first briefly review the solution of Z(2) kink solitons. Then we construct some multi-kink soliton configurations which are static and show their few features which are actually important to characterize their stability…
Focusing on multi-solitons for the Klein-Gordon equations, in first part of this paper, we establish their conditional asymptotic stability. In the second part of this paper, we classify pure multi-solitons which are solutions converging to…
We study a class of noncanonical real scalar field models in $(1+1)$-dimensional flat space-time. We first derive the general criterion for the classical linear stability of an arbitrary static soliton solution of these models. Then we…
The evolution of a universe with Brans-Dicke gravity and nonzero curvature is investigated here. We present the equations of motion and their solutions during the radiation dominated era. In a Friedman-Robertson-Walker cosmology we show…
We construct a new class of scalar noncommutative multi-solitons on an arbitrary Kahler manifold by using Berezin's geometric approach to quantization and its generalization to deformation quantization. We analyze the stability condition…
The self-consistent spatiotemporal evolution of drift wave (DW) radial envelope and zonal flow (ZF) amplitude is investigated in a slab model [1]. Stationary solution of the coupled partial differential equations in a simple limit yields…
We examine a collection of particles interacting with inverse-square two-body potentials in the thermodynamic limit. We find explicit large-amplitude density waves and soliton solutions for the motion of the system. Waves can be constructed…
We investigate whether the recently proposed PT-symmetric extensions of generalized Korteweg-de Vries equations admit genuine soliton solutions besides compacton solitary waves. For models which admit stable compactons having a width which…
We give arguments for the existence of {\it exact} travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a…
It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a…
Solitary waves, dubbed "solitons", are special types of waves that propagate for an infinite distance under ideal conditions. These waves are ubiquitously found in nature such as typhoon or neuron signals. Yet, their artificial generation…
We study large-amplitude, very oblique Alfv\'en waves at low $\beta$, with small gradient length scales, comparable to the ion inertial scale $d_i$. Such waves have large density fluctuations, and slight dispersion from finite-frequency and…
New boundary conditions are imposed on the familiar cylindrical gravitational wave vacuum spacetimes. The new spacetime family represents cylindrical waves in a flat expanding (Kasner) universe. Space sections are flat and nonconical where…
In this paper we prove the existence of vortices, namely standing waves with non null angular momentum, for the nonlinear Klein-Gordon equation in dimension $N\geq 3$. We show with variational methods that the existence of these kind of…