相关论文: A Novel Symmetry Constraint Of The Super cKdV Syst…

For the super AKNS system, an implicit symmetry constraint between the potentials and the eigenfunctions is proposed. After introducing some new variables to explicitly express potentials, the super AKNS system is decomposed into two…

The celebrated (1+1)-dimensional Korteweg de-Vries (KdV) equation and its (2+1)-dimensional extention, the Kadomtsev-Petviashvili (KP) equation, are two of the most important models in physical science. The KP hierarchy is explicitly…

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is…

We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2+1)-dimensional case and thereby propose a new…

This paper discusses the construction of a new $(3+1)$-dimensional Korteweg-de Vries (KdV) equation. By employing the KdV's recursion operator, we extract two equations, and with elemental computation steps, the obtained result is $…

We studied the constrained Hamiltonian formulation of a supersymmetric Korteweg-de Vries (KdV) equation, which is observed to be a constrained system similar to its classical version. We found a nontrivial Lagrangian description, where we…

In this paper we show that if one writes down the structure equations for the evolution of a curve embedded in an (n)-dimensional Riemannian manifold with constant curvature this leads to a symplectic, a Hamiltonian and an hereditary…

The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present…

We introduce a new generalization of matrix (1+1)-dimensional k-constrained KP hierarchy. The new hierarchy contains matrix generalizations of stationary DS systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik…

A supersymmetric breaking procedure for $N=1$ Super KdV, using a Clifford algebra, is implemented. Dirac's method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting…

For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1…

Completely integrable finite dimensional Hamiltonian systems are well understood thanks to the work of Liouville and Arnold. On the other hand, the Lax Pair formulation of the KdV equation marks the beginning of the extension of the…

An extension of the super Korteweg-de Vries integrable system in terms of operator valued functions is obtained. In particular the extension contains the $N=1$ Super KdV and coupled systems with functions valued on a symplectic space. We…

Starting from the complete integrable lattice super-KdV equation, two super-mappings are obtained by performing a travelling-wave reduction. The first one is linear and the second is a four dimensional super-QRT mapping containing both…

The existence of decompositions of the nonlinear integrable systems not only permits us to establish so-called linear superposition solutions but also to derive new nonlinear integrable coupled systems. Restricting our attention to the…

We construct a one-parameter family of N=3 supersymmetric extensions of the KdV equation as a Hamiltonian flow on N=3 superconformal algebra and argue that it is non-integrable for any choice of the parameter. Then we propose a modified N=3…

In this paper we present a set of results on the integration and on the symmetries of the lattice potential Korteweg-de Vries (lpKdV) equation. Using its associated spectral problem we construct the soliton solutions and the Lax technique…

Recently a new supersymmetric extension of the KdV hierarchy has appeared in a matrix-model-inspired approach to $2{-}d$ quantum supergravity. Here we prove that this hierarchy is essentially the KdV hierarchy, where the KdV field is now…

We present a notion of symmetry for 1+1-dimensional integrable systems which is consistent with their group theoretic description and reproduces in special cases the known Baecklund transformation for the generalized Korteweg-deVries…

We construct a new variety of $N=2$ supersymmetric integrable systems by junction of pseudo-differential superspace Lax operators for $a=4$, $N=2$ KdV and multi-component $N=2$ NLS hierarchies. As an important particular case, we obtain Lax…