相关论文: Constructing a Supersymmetric Integrable System fr…

Considering the coupled envelope equations in nonlinear couplers, the question of integrability is attempted. It is explicitly shown that Hirota's bilinear method is one of the simple and alternative techniques to Painlev\'e analysis to…

A supersymmetric breaking procedure for N=1 Super KdV, preserving the positivity of the hamiltonian as well as the existence of solitonic solutions, is implemented. The resulting integrable system is shown to have nice stability properties.

Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr\"oinger equation respectively. Multi-soliton solutions of the resulted…

The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral and apply the Mielnik's construction in supersymmetric…

In this talk we report some results about the construction of soliton solutions for the Affine and Conformal Affine Toda models using the Hirota's method. We obtain new classes of solitons connected to the degeneracies of the Cartan matrix…

Contrary to the common understanding, the Sine-Gordon equation in (1+2) dimensions does have N-soliton solutions for any N. The Hirota algorithm allows for the construction of static N-soliton solutions (i.e., solutions that do not depend…

Manifest N=2 supersymmetric Toda systems are constructed from the $sl(n,n+1)$ superalgebras by taking into account their complex structure. In the $n\to \infty$ continuum limit an N=2 extension of the $(2+1)$-dimensional heavenly equation…

We prove that Mathieu's N=2 supersymmetric Korteweg-de Vries equations with a=1 or a=4 admit Hirota's n-supersoliton solutions, whose nonlinear interaction does not produce any phase shifts. For initial profiles that can not be…

A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all…

We discuss the ways of constructing the exact superpotential for N=1 supersymmetric theories and propose a new approach. As a consequence, a new structure of the superpotential is found.

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…

An N=1 supersymmetric extension of the Ruijsenaars-Schneider three-body model is constructed and its integrability is established. In particular, three functionally independent Grassmann-odd constants of the motion are given and their…

We construct super Hamiltonian integrable systems within the theory of Supersymmetric Poisson vertex algebras (SUSY PVAs). We provide a powerful tool for the understanding of SUSY PVAs called the super master formula. We attach some Lie…

The Poisson structure of a coupled system arising from a supersymmetric breaking of N=1 Super KdV equations is obtained. The supersymmetric breaking is implemented by introducing a Clifford algebra instead of a Grassmann algebra. The…

A few new N=2 superintegrable mappings in the (1|2) superspace are proposed and their origin is analyzed. Using one of them, acting like the discrete symmetry transformation of the N=2 supersymmetric modified NLS hierarchy, the recursion…

Bright plane soliton solutions of an integrable (2+1) dimensional ($n+1$)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one…

Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials W(x)=2/x, W(x)=2/sin(x), and W(x)=2/sinh(x) is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd…

We generalize the Drinfeld-Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in…

In this paper we present a simple, algorithmic test to establish if a Hamiltonian system is maximally superintegrable or not. This test is based on a very simple corollary of a theorem due to Nekhoroshev and on a perturbative technique…

We investigate existence of solitonic solutions for higher-order partial differential equations with polynomial nonlinearities. Using the Hirota method we obtain classification for higher-order integrable systems of equations.