相关论文: Lax-Sato formulation of the Novikov-Veselov Hierar…

We construct B\"acklund transformations (BT) for the Gelfand-Dickey hierarchy (GD$_n$-hierarchy) on the space of $n$-th order differential operators on the line. Suppose $L=\partial_x^n-\sum_{i=1}^{n-1}u_i\partial_x^{(i-1)}$ is a solution…

The discrete symmetry transformations of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed. Their bosonic limit is analyzed and new discrete symmetries of the modified GNLS hierarchy are derived. The explicit relations connecting…

We present the Lax operator for the N=3 KdV hierarchy and consider its extensions. We also construct a new infinite family of N=2 supersymmetric hierarchies by exhibiting the corresponding super Lax operators. The new realization of N=4…

We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are…

We develop an abstract theory of flows of geometric $H$-structures, i.e., flows of tensor fields defining $H$-reductions of the frame bundle, for a closed and connected subgroup $H\subset SO(n)$, on any connected and oriented $n$-manifold…

The set of integrable symmetries of the nonstationary Schr\"{o}dinger equation is shown to admit a natural decomposition into subsets of mutually commuting symmetries. Hierarchies of time evolutions associated with each of these subsets…

We develop the inverse scattering transform method for the Novikov equation $u_t-u_{txx}+4u^2u_x=3u u_xu_{xx}+u^2u_{xxx}$ considered on the line $x\in(-\infty,\infty)$ in the case of non-zero constant background. The approach is based on…

The extended flow equations of a new $Z_N$-Toda hierarchy which takes values in a commutative subalgebra $Z_N$ of $gl(N,\mathbb C)$ is constructed. Meanwhile we give the Hirota bilinear equations and tau function of this new extended…

This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of functionals along flows defined by some nonlinear diffusion equations…

We construct Orlov-Schulman symmetries for the self-dual conformal structure (SDCS) hierarchy. We provide an explicit proof of compatibility of additional symmetries with the basic Lax-Sato flows of the hierarchy, and consider several…

A coupled Camassa-Holm type equation is linked to the first negative flow of a modified Drinfeld-Sokolov III hierarchy by a transformation of reciprocal type. Meanwhile the Lax pair and bi-Hamiltonian structure behaviors of this coupled…

Building on a recent work of \v C. Crnkovi\'c, M. Douglas and G. Moore, a study of multi-critical multi-cut one-matrix models and their associated $sl(2,C)$ integrable hierarchies, is further pursued. The double scaling limits of hermitian…

We introduce two families of soliton hierarchies: the twisted hierarchies associated to symmetric spaces. The Lax pairs of these two hierarchies are Laurent polynomials in the spectral variable. Our constructions gives a hierarchy of…

The first example of the so-called "coupled" integrable hydrodynamic chain is presented. Infinitely many commuting flows are derived. Compatibility conditions of the first two of them lead to the remarkable Manakov--Santini system.…

In this paper we study commuting difference operators of rank two. We introduce an equation on potentials $V(n),W(n)$ of the difference operator $L_4=(T+V(n)T^{-1})^2+W(n)$ and some additional data. With the help of this equation we find…

It has been proved by V. Sokolov that the Krichever-Novikov equation's hierarchy is hamiltonian for the non-local Hamiltonian operator H_0=u_x D^{-1} u_x and possesses twi weakly non-local recursion operatos of degree 4 and 6, L_4 and L_6.…

A vector calculus approach for the determination of advected invariants is presented for inviscid fluid flow. This approach describes invariants by means of Lie dragging of scalars, vectors, and skew-tensors with respect to the fluid…

Let A be a nonassociative algebra such that the associator (A,A^2,A) vanishes. If A is freely generated by an element f, there are commuting derivations delta_n, n=1,2,..., such that delta_n(f) is a nonlinear homogeneous polynomial in f of…

We consider N=2 supergravity in four dimensions, coupled to an arbitrary number of vector- and hypermultiplets, where abelian isometries of the quaternionic hyperscalar target manifold are gauged. Using a static and spherically or…

In this work we present an application of a theory of vessels to solution of the evolutionary Non Liner Schrodinger (NLS) equation. The classes of functions for which the initial value problem is solvable relies on the existence of an…