O ct 2 00 3 On two recent generalizations of the Harry Dym equation
نویسنده
چکیده
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.
منابع مشابه
ct 2 00 3 Transformation of a generalized Harry Dym equation into the Hirota – Satsuma system
The new generalized Harry Dym equation of Z. Popowicz is transformed into the Hirota–Satsuma system of coupled KdV equations.
متن کاملN ov 2 00 3 Transformation of a generalized Harry Dym equation into the Hirota – Satsuma system
The new generalized Harry Dym equation, recently introduced by Z. Popowicz in Phys. Lett. A 317, 260–264 (2003), is transformed into the Hirota–Satsuma system of coupled KdV equations.
متن کاملDerivation and implicit solution of the Harry Dym equation and its connections with the Korteweg - de Vries equation
The Harry Dym equation, which is related to the classical string problem, is derived in three different ways. An implicit cusp solitary-wave solution is constructed via a simple direct method. The existing connections between the Harry Dym and the Kortwegde Vries equations are uniformised and simplified, and transformations between their respective solutions are carried out explicitly. Whenever...
متن کاملOn the Bi-hamiltonian Theory for the Harry Dym Equation
We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg-de Vries equation and other soliton equations. This is achieved by means of a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev-Petviashivili hierarchy whose reduction leads to the Harry Dym hierarchy. We call such system the HD-KP hi...
متن کاملBi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy
We study the Harry Dym hierarchy of nonlinear evolution equations from the bi-Hamiltonian view point. This is done by using the concept of an S-hierarchy, which permits us to define a matrix Harry Dym hierarchy. We conclude by showing that the conserved densities of the matrix Harry Dym equation can be found by means of a Riccati-type equation.
متن کامل