Journal of Nonlinear Mathematical Physics

In this paper, we construct Darboux transformations of the supersymmetric BKP(SBKP) hierarchy. These Darboux transformations can generate new solutions from seed solutions by using bosonic eigenfunctions.

In this paper we derive generalized forms of the Camassa-Holm (CH) equation from a Boussinesq-type equation using a two-parameter asymptotic expansion based on two small parameters characterizing nonlinear and dispersive effects and strictly following the arguments in the asymptotic derivation of the...

In this paper, some properties of tensor fields constructed by the Lax representation of chiral-type systems are investigated.

The Heisenberg supermagnet model which is the supersymmetric generalization of the Heisenberg ferromagnet model is an important integrable system. We consider the deformations of Heisenberg supermagnet model under the two constraint 1. S2 = S for S ∈ USPL(2/1)/S(L(1/1) × U(1)) and 2. S2 = 3S − 2I S ∈...

In this short communication, we want to pay attention to a few wrong formulas which are unfortunately cited and used in a dozen papers afterwards. We prove that the provided relations and asymptotic expansion about the q-gamma function are not correct. This is illustrated by numerous concrete counterexamples....

The necessary and sufficient conditions for a hyperbolic semi-discrete equation to have five dimensional characteristic x-ring are derived. For any given chain, the derived conditions are easily verifiable by straightforward calculations.

The noncommutative Toda hierarchy is studied with the help of Moyal deformation by a reduction on the non-commutative two dimensional Toda hierarchy. Further we generalize the noncommutative Toda hierarchy to the extended noncommutative Toda hierarchy. To survey on its integrability, we construct the...

The symmetry constraint for dispersionless Harry Dym (dHD) hierarchy is derived for the first time by taking dispersionless limit of that for 2+1 dimensional Harry Dym hierarchy. Then, the dHD is extended by means of the symmetry constraint which we derived. From the zero-curvature equation of the new...

We study a simple nonlinear model defined on the honeycomb and triangular lattices. We propose a bilin-earization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the Hirota bilinear difference equation and the Ablowitz-Ladik...

This paper is concerned with orbital stability of the smooth solitary wave with nonzero asymptotic value for the mCH equation ut−uxxt+2kux+au2ux=2uxuxx+uuxxx. Under the parametric conditions a > 0 and k<18a , an interesting phenomenon is discovered, that is, for the stability there...

We investigate the existence of several families of symmetric periodic solutions as continuation of circular orbits of the Kepler problem for certain symmetric differentiable perturbations using an appropriate set of Poincaré-Delaunay coordinates which are essential in our approach. More precisely, we...