Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy, are transformed into previously known integrable systems: one—into a pair of decoupled KdV equations , the other one—into a pair of coupled mKdV equations from a bi-Hamiltonian hierarchy of Kupershmidt.

We study a generalization of the hierarchy of mKdV equations (modi-ed KdV), which forms an integrable system. This generalization is based on a Lax operator associated to the equations, with principal components of degrees between ?3 and 0. The main result of the study is the com-mutation of the classical integrals of motion. For that purpose, one can construct an isomorphism between the space ...

We study well-posedness of the complex-valued modified KdV equation (mKdV) on real line. In particular, we prove local mKdV in modulation spaces \begin{document}$ M^{2,p}_{s}( \mathbb{R}) $\end{document} for id="M2">\begin{document}$ s \ge \frac14 and id="M3">\begin{document}$ 2\leq p < \infty $\end{do...

The propagation of linear and nonlinear electron acoustic waves (EAWs) in an unmagnetized plasma, comprising dynamical inertial electrons, hot ( r , q ) distributed warm beam, immobile ions is studied. dispersion relation investigated for varying beam velocity. Korteweg-de Vries (KdV) equation EAWs derived the small amplitude limit. Depending on density, temperature velocity, we get a critical ...