相关论文: B\"acklund Transformations and Loop Group Actions
We establish the pluri-Lagrangian structure for families of B\"acklund transformations of relativistic Toda-type systems. The key idea is a novel embedding of these discrete-time (one-dimensional) systems into certain two-dimensional…
We explain how to apply techniques from integrable systems to construct $2k$-soliton homoclinic wave maps from the periodic Minkowski space $S^1\times R^1$ to a compact Lie group, and more generally to a compact symmetric space. We give a…
A map is presented that associates with each element of a loop group a solution of an equation related by a simple change of coordinates to the Camassa-Holm (CH) Equation. Certain simple automorphisms of the loop group give rise to Backlund…
We investigate strictly developable simple complexes of groups with arbitrary local groups, or equivalently, group actions admitting a strict fundamental domain. We introduce a new method for computing the cohomology of such groups. We also…
To any action of a compact quantum group on a von Neumann algebra which is a direct sum of factors we associate an equivalence relation corresponding to the partition of a space into orbits of the action. We show that in case all factors…
Starting from the functional representation of the Ablowitz-Kaup-Newell-Segur (AKNS) and derivative nonlinear Schr\"odinger (DNLS) hierarchies and using the chains of the Miura-like transformations we derive a set of B\"acklund…
The construction of generalized Backlund transformation for the $A_n$ Affine Toda hierarchy is proposed in terms of gauge transformation acting on the zero curvature representation. Such construction is based upon the graded structure of…
The construction of Miura and B\"acklund transformations for $A_n$ mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in the well known $sl(2)$ case, we derive and…
We show that the finite difference B\"acklund formula for the Schr\"odinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered by two of us in a previous paper. Then, we give a group…
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…
A generalized moment map is proposed for arbitrary symplectic actions of compact connected Lie groups on closed symplectic manifolds, in the spirit of the circle -valued maps introduced by D. McDuff in the case of non-Hamiltonian circle…
In this work we show that, under certain conditions, parametric Backlund transformations (BTs) for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous…
We consider a class of finite-dimensional dynamical systems whose equations of motion are derived from a non-local-in-time action principle. The action functional has a zeroth order piece derived from a local Hamiltonian and a perturbation…
Conservation laws, heirarchies, scattering theory and B\"acklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a theory of Poisson group actions, and apply…
We introduce a practical construction of group-equivariant and permutation-invariant functions of $N$ variables given a finite-dimensional space stable with respect to the group action. The construction applies to any connected linear Lie…
New infinite number of one- and two-point B\"{a}cklund transformations (BTs) with explicit expressions are constructed for the high-order constrained flows of the AKNS hierarchy. It is shown that these BTs are canonical transformations…
We present the third in the series of papers describing Poisson properties of planar directed networks in the disk or in the annulus. In this paper we concentrate on special networks N_{u,v} in the disk that correspond to the choice of a…
A group action on the input ring or category induces an action on the algebraic $K$-theory spectrum. However, a shortcoming of this naive approach to equivariant algebraic $K$-theory is, for example, that the map of spectra with $G$-action…
We classify the simplest rational elements in a twisted loop group, and prove that dressing actions of them on proper indefinite affine spheres give the classical Tzitz\'eica transformation and its dual. We also give the group point of view…
The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type, in an iterated sense,…