Related papers: An Exactly Solvable Case for a Thin Elastic Rod
In the present work we discuss non-linear physics problems such as Nielsen-Olesen strings, superconducting bosonic straight strings and static vortex rings. We start with a toy model. We search for antiperiodic solitons of the Goldstone…
We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near…
We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
We consider the Landau-Lifshitz equation for the spin torque oscillator - a uniaxial ferromagnet in an external magnetic field with polarised spin current driven through it. In the absence of the Gilbert damping, the equation turns out to…
We define combinatorial analogues of stable and unstable minimal surfaces in the setting of weighted pseudomanifolds. We prove that, under mild conditions, such combinatorial minimal surfaces always exist. We use a technique, adapted from…
In this paper, we are concerned with the existence of invariant curves of the planar twist mappings where the perturbations are almost periodic. As an application, the existence of almost periodic solutions and the boundedness of all…
We study the elastic response of composites of rods embedded in elastic media. We calculate the micro-mechanical response functions, and bulk elastic constants as functions of rod density. We find two fixed points for Poisson's ratio with…
We consider the rotating and translating equilibria of open finite vortex sheets with endpoints in two-dimensional potential flows. New results are obtained concerning the stability of these equilibrium configurations which complement…
We study the gradient flow of Spin($7$)-structures and construct the first explicit solutions, in the homogeneous setting. As an intermediate step, we obtain formulae expressing the Spin($7$)-torsion tensor and gradient flow in terms of the…
We prove the existence of at least two geometrically different periodic solution with winding number N for the forced relativistic pendulum. The instability of a solution is also proved. The proof is topological and based on the version of…
We prove well-posedness, partial regularity, and stability of the thin-film equation $h_t + (m(h) h_{zzz})_z = 0$ with general mobility $m(h) = h^n$ and mobility exponent $n\in (1,\tfrac{3}{2})\cup (\tfrac{3}{2},3)$ in the regime of perfect…
The vortex-like solutions are studied in the framework of the gauge model of disclinations in elastic continuum. A complete set of model equations with disclination driven dislocations taken into account is considered. Within the linear…
In this paper we apply a nonconforming rotated bilinear tetrahedral element to the Stokes problem in $\mathbb{R}^3$. We show that the element is stable in combination with a piecewise linear, continuous, approximation of the pressure. This…
This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon…
This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single…
The goal of this paper is to investigate some rigidity properties of stable solutions of elliptic equations set on manifolds with boundary. We provide several types of results, according to the dimension of the manifold and the sign of its…
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…
In both the Gardner equation and its extensions, the non-convex convection bounds the range of solitons / compactons velocities beyond which they dissolve and kink/anti-kink form. Close to solitons barrier we unfold a narrow strip of…
We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions…