We derive a new zero-curvature formalism for the sine-Gordon (sG) equation which permits the introduction of a local sine-Gordon hierarchy (in contrast to the traditionally accepted nonlocal higher-order sG equations). In complete analogy to other completely integrable hierarchies of soli-ton equations, such as the KdV, AKNS, and Toda hierarchies, our local sG hierarchy is recursively construct...

An approximate method for describing the evolution of solitonlike initial conditions to solitons for the sine-Gordon equation is developed. This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian is then used to determine ordinary differential equations governing the evolution of the pulse parame...

The relationship between the soliton dynamics provided by the classical sine-Gordon and massive Thirring models is exhibited. Solitons are characterized as classical relativistic particles through the consideration of their associated canonical realizations of the Poincare group. It is shown that the soliton in the massive Thirring model determines two different kinds of relativistic particles ...

As I briefly review, the sine-Gordon model may be obtained by dimensional and algebraic reduction from 2+2 dimensional self-dual U(2) Yang-Mills through a 2+1 dimensional integrable U(2) sigma model. I argue that the noncommutative (Moyal) deformation of this procedure should relax the algebraic reduction from U(2) → U(1) to U(2) → U(1)×U(1). The result are novel noncommutative sine-Gordon equa...

Among various barycentric coordinates and their extensions, the linear and cubic (Hermite) Gordon-Wixom transfinite interpolation schemes deliver the most accurate approximations of the harmonic and biharmonic functions, respectively. However interpolation properties of the original Gordon-Wixom interpolations are studied for convex domains only and, therefore, their current practical importanc...

We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modi-ed Korteweg{de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations, such as the KdV, AKNS, and Toda hierarchies, the sGmKdV hierarchy is recursively constructed by means of a fundamental polynomial formalism involving a spectr...