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...

We prove a global Birkhoff decomposition for almost split real forms of loop groups, when an underlying finite dimensional Lie group is compact. Among applications, this shows that the dressing action by the whole subgroup of loops which extend holomorphically to the exterior disc on the U -hierarchy of the ZS-AKNS systems, on curved flats and on various other integrable systems, is global for ...

We construct the classical Poisson structure and r-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the r-matrices associated with the constrained flows of the Kaup-Newell, KdV...

We study the motion of surfaces in an intrinsic formulation in which the surface is described by its metric and curvature tensors. The evolution equations for the six quantities contained in these tensors are reduced in number in two cases: (i) for arbitrary surfaces, we use principal coordinates to obtain two equations for the two principal curvatures, highlighting the similarity with the equa...

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by viscosity. This is derived in Riemann variables using a modified finite-gap integration technique for the Ablowitz-Kaup-Newell...

بناهایفرم مفهومی پویا و لغزان است که از هریک گفتمان‌های مختلف معماری تلقی متفاوتی آن به‌دست آمده است. در این مقاله با هدف بازاندیشی مفهومِ فرم گفتمان معاصر، به تبیین زیربنای نظری اقتضائات قابلیت پرداخته شده بدین منظور نخست برخی نیروهای بنیادین مؤثر بر تحول مفهوم دوران معاصر شناسایی شده‌اند؛ سپس به‌مثابة تلقی‌ای پاسخ‌گویی ذکرشده را ممکن می‌کند، معرفی گردیده است؛ ادامه حضور طریق بسط نوشتار مسیر مع...