Related papers: Hylomorphic solitons for the generalized KdV equat…
Under the effect of common perturbations, the multiple-soliton solution of the KdV equation is transformed into a sum of an elastic and a first-order inelastic component. The elastic component is a perturbation series, identical in…
Hamilton flows on K\"ahler manifold for which all trajectories are $H$-planar curves (complex analog of geodesics) are considered. These flows are called $H$-planar. The equation which has to obey the Hamiltonian of $H$-planar Hamilton flow…
We consider the existence and stability of solitons in generalized galileons, scalar field theories with higher-derivative interactions but second-order equations of motion. It has previously been proven that no stable, static solitons…
Using a quasi-linear version of Hodge theory, holomorphic vector bundles in a neighbourhood of a given polystable bundle on a compact Kaehler manifold are shown to be (poly)stable if and only if their corresponding classes are (poly)stable…
In this paper we study the stability problem for KdV solitons on the left and right half-line. Unlike standard KdV, these are not exact solutions to the equations posed in the half-line. However, we are able to show that solitons placed…
A theory for constructing integrable couplings of soliton equations is developed by using various perturbations around solutions of perturbed soliton equations being analytic with respect to a small perturbation parameter. Multi-scale…
Solitary wave and soliton solutions of nonlinear equations are well known for physicists. A soliton is a solitary wave with some outstanding features which make it reasonable to be studied seriously in nonlinear systems. In fact most of the…
Harmonically modulated complex solitary waves which are a generalized type of envelope soliton (herein coined oscillatory solitons) are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries…
We demonstrate the existence of complex solitary wave and periodic solutions of the Kortweg de-vries (KdV) and modified Kortweg de-Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are…
In this article we classify solitons (equilibria, self-similar solutions and travelling waves) for the surface diffusion flow of entire graphs of function over the real line.
A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…
We introduce discrete multivortex solitons in a ring of nonlinear oscillators coupled to a central site. Regular clusters of discrete vortices appear as a result of mode collisions and we show that their stability is determined by global…
We consider the generalized Korteweg-de Vries equation \partial_t u + \partial_x (\partial_x^2 u + f(u))=0, \quad (t,x)\in [0,T)\times \mathbb{R}, (1) with general $C^3$ nonlinearity $f$. Under an explicit condition on $f$ and $c>0$, there…
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small…
We consider the nonlinear Klein-Gordon equation in $\R^d$. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the…
The long-time evolution of the KdV-type solitons propagating in ferromagnetic materials is considered trough a multi-time formalism, it is governed by all equations of the KdV Hierarchy. The scaling coefficients of the higher order time…
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…
Soliton gas or soliton turbulence is a subject of intense studies due to its great importance to optics, hydrodynamics, electricity, chemistry, biology and plasma physics. Usually, this term is used for integrable models where solitons…
We study dynamics of dark solitons in the theory of the DNLS equation by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes' remark that relationships for harmonic linear…
Formation of oblique solitons by a flow of polariton condensate past an obstacle is considered. The flow is non-uniform due to a finite life-time of polaritons what changes drastically the conditions of formation of oblique solitons…