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...

Jednym z głównych pytań w filozofii logiki jest to, czy jedna, wiele logik. Pytanie to doczekało się różnych odpowiedzi, które formułują opozycyjne stanowiska: monizm logiczny contra pluralizm logiczny. Za reprezentatywnego przedstawiciela monizmu uznawany Willard Van Orman Quine, a pluralizmu — Susan Haack. Oba te stanowiska są kontynuowane współcześnie: (m.in. Michael Dummett, Graham Priest, ...

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 ...

The following problem was raised in a paper by Dan Willard [6]: Given n points (ai, bi) (i = 1,. . . , n), find two straight lines that partition the plane in such a way that each (closed) quadrant contains at least /n/4] points. Cole, Sharir, and Yap [l] propose an algorithm which is based on the scheme for applying parallel algorithms in the design of serial ones that is presented in [3]. The...

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...