Related papers: On UrKdV and UrKP
We show that any multi-component matrix KP hierarchy is equivalent to the standard one-component (scalar) KP hierarchy endowed with a special infinite set of abelian additional symmetries, generated by squared eigenfunction potentials. This…
Using a multicomponent version of the CKP hierarchy we construct the prepotential of the WDVV equations.
Recent work in the field of signal processing has shown that the singular value decomposition of a matrix with entries in certain real algebras can be a powerful tool. In this article we show how to generalise the QR decomposition and SVD…
Using the Weiss method of truncated singular expansions, we construct an explicit Backlund transformation of the Drinfeld-Sokolov-Satsuma-Hirota system into itself. Then we find all the special solutions generated by this transformation…
We study the plus and minus type discrete mKdV equation. Some different symmetry conditions associated with two Lax pairs are introduced to derive the matrix Riemann-Hilbert problem with zero. By virtue of regularization of the…
We consider a class of third-order evolution equations of the form \begin{equation*} \left\{ \begin{array}{l} \displaystyle u_{t}=F\left(x,t,u,u_x,u_{xx},u_{xxx},v,v_x,v_{xx},v_{xxx}\right), \displaystyle…
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper…
We connect the dual adjunction between MV-algebras and Tychonoff spaces with the general theory of natural dualities, and provide a number of applications. In doing so, we simplify the aforementioned construction by observing that there is…
The modified Korteweg-de Vries hierarchy (mKdV) is derived by imposing isometry and isoenergy conditions on a moduli space of plane loops. The conditions are compared to the constraints that define Euler's elastica. Moreover, the conditions…
It is shown that there exists two inner authomorpism which lead to different form of the sistems equations of integrable hierarchy. We present discrete and Backlund transformation connected with such systems and a general formula for…
An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of…
The deformed double covering of E(2) group, denoted by $\tilde{E}_\kappa(2)$, is obtained by contraction from the $SU_\mu(2)$. The contraction procedure is then used for producing a new examples of differential calculi: 3D-left covariant…
A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based…
The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring D generated by commuting derivations. A D-free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit…
We construct Darboux transformations for the super-symmetric KP hierarchies of Manin--Radul and Jacobian types. We also consider the binary Darboux transformation for the hierarchies. The iterations of both type of Darboux transformations…
We illustrate the basic notions of {\em additional non-isospectral symmetries} and their interplay with the discrete {\em \DB transformations} of integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili} (\cKP)…
On base of three-dimensional flat metrics obtained with the help of solutions of the KdV-equation were constructed the examples of six-dimensional metrics, which are determined by the help of solutions of Krichever-Novikov and KdV. Their…
The relation between the infinite-dimensional 3-algebras and the dispersionless KdV hierarchy is investigated. Based on the infinite-dimensional 3-algebras, we derive two compatible Nambu Hamiltonian structures. Then the dispersionless KdV…
This paper provides a systematic description of the interplay between a specific class of reductions denoted as \cKPrm ($r,m \geq 1$) of the primary continuum integrable system -- the Kadomtsev-Petviashvili ({\sf KP}) hierarchy and discrete…
A short proof is given to the fact that the additional symmetries of the KP hierarchy defined by their action on pseudodifferential operators, according to Fuchssteiner-Chen-Lee-Lin-Orlov-Shulman, coincide with those defined by their action…