Related papers: Solitons in a 3d integrable model
The most general Lagrangian for non-linear electrodynamics coupled to an axion $a$ and a dilaton $\phi$ with $SL(2,\mbox{\elevenmsb R})$ invariant equations of motion is $$ -\half\left(\nabla\phi\right)^2 - \half e^{2\phi}\left(\nabla…
We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and…
We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…
A modification of the usual Type-II second-harmonic-generation model is proposed, which includes two additional features: linear conversion and walkoff (group-velocity difference) between two components of the fundamental-frequency (FF)…
We propose a consistent expression for the relativistic quadri-force referring to the classical interaction between a coloured particle and a scalar field multiplete. General aspects of the resultant equations of motion are discussed as…
The purpose of this paper is to propose a revised continuum model from the discrete system introduced in [Deng et.al., PRL, 2017] . Using a Galilean transformation, we obtain an equation governing the soliton solutions in the phase plane -…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
I introduce an extended configuration space for classical mechanical systems, called pair-space, which is spanned by the relative positions of all the pairs of bodies. To overcome the non-independence of this basis, one adds to the…
The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy's Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification…
We study the gauged Landau-Lifshitz model in which a suitably chosen triplet of background scalar fields is included. It is shown that the model admits solitonic configurations.
The solitaire of independence is a groupoid action resembling the classical 15-puzzle, which gives information about independent sets of coordinates in a totally extremally permutive subshift. We study the solitaire with the triangle shape,…
In this paper, we study the equations of motion for non-Abelian N=(2,0) tensor multiplets in six dimensions, which were recently proposed by Lambert and Papageorgakis. Some equations are regarded as constraint equations. We employ a loop…
Variational integrators applied to degenerate Lagrangians that are linear in the velocities are two-step methods. The system of modified equations for a two-step method consists of the principal modified equation and one additional equation…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…
We reconsider the construction of solitons by dressing transformations in the sine-Gordon model. We show that the $N$-soliton solutions are in the orbit of the vacuum, and we identify the elements in the dressing group which allow us to…
Recent work in the literature has advocated using the Earth-Moon-planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body…
The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non--abelian theories. Possible applications of these solutions to…
Massive integrable field theories in $1+1$ dimensions are defined at the Lagrangian level, whose classical equations of motion are related to the ``non-abelian'' Toda field equations. They can be thought of as generalizations of the…