Related papers: Comments on the negative grade KdV hierarchy
In this paper we consider the ${\cal N}=1$ supersymmetric mKdV hierarchy composed of positive odd flows embedded within an affine $\hat sl(2,1)$ algebra. Its B\"acklund transformations are constructed in terms of a gauge transformation…
The gauge equivalence between basic KP hierarchies is discussed. The first two Hamiltonian structures for KP hierarchies leading to the linear and non-linear $\Winf$ algebras are derived. The realization of the corresponding generators in…
The construction of a nonautonomous mixed mKdV/sine-Gordon model is proposed by employing an infinite dimensional affine Lie algebraic structure within the zero curvature representation. A systematic construction of soliton solutions is…
The main object of this paper is to produce a deformation of the KdV hierarchy of partial differential equations. We construct this deformation by taking a certain limit of the Toda hierarchy. This construction also provides a deformation…
A complete algorithm is developed to deduce quasi-periodic solutions for the negative-order KdV (nKdV) hierarchy by using the backward Neumann systems. From the nonlinearization of Lax pair, the nKdV hierarchy is reduced to a family of…
A KdV flow is constructed on a space whose structure is described in terms of the spectrum of the underlying Schr\"odinger operators. The space includes the conventional decaying functions and ergodic ones. Especially any smooth almost…
Higher KdV flows on spaces of closed equicentroaffine plane curves are studied and it is shown that the flows are described as certain multi-Hamiltonian systems on the spaces. Multi-Hamiltonian systems describing higher mKdV flows are also…
We derive the entire KdV hierarchy as well as the recursion relations from the self-duality condition on gauge fields in four dimensions.
The solutions of a large class of hierarchies of zero-curvature equations that includes Toda and KdV type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras~$\ggg$.…
The dynamics of the highly nonlinear fifth order $KdV$-type equation is discussed in the framework of the Lagrangian and Hamiltonian formalisms. The symmetries of the Lagrangian produce three commuting conserved quantities that are found to…
It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector…
We consider the nonstandard constrained KP (ncKP) hierarchy which is obtained from the multi-constraint KP hierarchy by gauge transformation. The second Hamiltonian structure of the ncKP hierarchy can be simplified by factorizing the Lax…
We generalize the dressing symmetry construction in mKdV hierarchy. This leads to non-local vector fields (expressed in terms of vertex operators) closing a Virasoro algebra. We argue that this algebra realization should play an important…
Using bidifferential calculus, we derive a vectorial binary Darboux transformation for the first member of the "negative" part of the AKNS hierarchy. A reduction leads to the first "negative flow" of the NLS hierarchy, which in turn is a…
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 matrix 2x2 spectral differential equation of the second order is considered on x in ($-\infty,+\infty$). We establish elementary Darboux transformations covariance of the problem and analyze its combinations. We select a second…
A one-parameter generalization of the hierarchy of negative flows is introduced for integrable hierarchies of evolution equations, which yields a wider (new) class of non-evolutionary integrable nonlinear wave equations. As main results,…
From an algebraic construction of the mKdV hierarchy we observe that the space component of the Lax operator play a role of an universal algebraic object. This fact induces the universality of a gauge transformation that relates two field…
We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized…
The matrix 2x2 spectral differential equation of the second order is considered on x in ($-\infty,+\infty$). We establish elementary Darboux transformations covariance of the problem and analyze its combinations. We select a second…