Related papers: Negative order MKdV hierarchy and a new integrable…
We discuss the integrable hierarchies that appear in multi--matrix models. They can be envisaged as multi--field representations of the KP hierarchy. We then study the possible reductions of this systems via the Dirac reduction method by…
A class of negative order Ablowitz--Kaup--Newell--Segur nonlinear evolution equations are obtained by applying the Lax hierarchy of the first order linear system of three equations. The inverse scattering problem on the whole axis are…
Employing the Hirota's method, a class of soliton solutions for the N=2 super mKdV equations is proposed in terms of a single Grassmann parameter. Such solutions are shown to satisfy two copies of N=1 supersymmetric mKdV equations connected…
The negative symmetry flows are incorporated into the Riemann-Hilbert problem for the homogeneous $A_m$-hierarchy and its $\hat{gl} (m+1, C)$ extension. A loop group automorphism of order two is used to define a sub-hierarchy of $\hat{gl}…
New reductions for the multicomponent modified Korteveg-de Vries (MMKdV) equations on the symmetric spaces of {\bf DIII}-type are derived using the approach based on the reduction group introduced by A.V. Mikhailov. The relevant inverse…
Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax…
We discuss a differential integrable hierarchy, which we call the (N, M)$--th KdV hierarchy, whose Lax operator is obtained by properly adding $M$ pseudo--differential terms to the Lax operator of the N--th KdV hierarchy. This new hierarchy…
Starting with Lagrangians, which turn out to be degenerate, the Hamiltonian operators for integrable systems can be constructed using Dirac's theory of constraints. We illustrate this by giving a systematic discussion of the first…
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…
Inspired by the forms of delay-Painleve equations, we consider some new differential-discrete systems of KdV, mKdV and Sine-Gordon - type related by simple one way Miura transformations to classical ones. Using Hirota bilinear formalism we…
A moving frame formulation of geometric non-stretching flows of curves in the Riemannian symmetric spaces $Sp(n+1)/Sp(1)\times Sp(n)$ and $SU(2n)/Sp(n)$ is used to derive two bi-Hamiltonian hierarchies of symplectically-invariant soliton…
We study a nonsmooth nonconvex optimization problem defined over nonconvex constraints, where the feasible set is given by the intersection of the closure of an open set and a smooth manifold. By endowing the open set with a Riemannian…
An eigenvalue problem with a reference function and the corresponding hierarchy of nonlinear evolution equations are proposed. The bi-Hamiltonian structure of the hierarchy is established by using the trace identity. The isospectral problem…
The goal of this paper is to give a representation-theoretic interpretation of the sine-Gordon equation. We consider a vertex operator representation of affine Kac-Moody algebra \hat{sl_2} on the space of differential operators. In this…
The aim of this article is twofold: one one side we introduce and study the properties of a critical sinh-Gordon type flow \begin{equation*} {\frac{\partial}{\partial…
When both Hamiltonian operators of a bi-Hamiltonian system are pure differential operators, we show that the generalized Kupershmidt deformation (GKD) developed from the Kupershmidt deformation in \cite{kd} offers an useful way to construct…
The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the $\wp$-functions that uniformize the associated spectral curve. Quasi-periodic solutions to the…
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,…
In this paper, we construct the additional flows of the noncommutative Kadomtsev-Petviashvili(KP) hierarchy and the additional symmetry flows constitute an infinite dimensional Lie algebra $W_{1+\infty}$. In addition, the generating…
We constructed the three nonequivalent gradings in the algebra $D_4 \simeq so(8)$. The first one is the standard one obtained with the Coxeter automorphism $C_1=S_{\alpha_2} S_{\alpha_1}S_{\alpha_3}S_{\alpha_4}$ using its dihedral…