Miura type transformations and homogeneous spaces

The Boussinesq equation and Miura type transformations

Several Miura type transformations for the Boussinesq equation are found and the corresponding integrable systems constructed.

Approach to Discrete Miura Transformations

We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of τ-functions. Elimination of τ-functions from the resulting system leads to another nonlinear equation, which is a " modified " version of the original equation....

The Cole-hopf and Miura Transformations Revisited

An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura's transformation connecting the KdV and mKdV equations is studied in detail. 1. Introduction Our aim in this note is to display the close similarity between the well-known Cole{Hopf transformation relating the Burgers and the heat equation, and the celebrated Miura trans...

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces