In this letter, a definition of the higher dimensional Lax pair for a lower dimensional system which may be a chaotic system is given. A special concrete (2+1)-dimensional Lax pair for a general (1+1)-dimensional three order autonomous partial differential equation is studied. The result shows that any (1+1)-dimensional three order semi-linear autonomous system (no matter it is integrable or no...

The space-time monopole equation is obtained from a dimension reduction of the anti-self dual Yang-Mills equation on R. A family of Ward equations is obtained by gauge fixing from the monopole equation. In this paper, we give an introduction and a survey of the space-time monopole equation. Included are alternative explanations of results of Ward, Fokas-Ioannidou, Villarroel and Zakhorov-Mikhai...

Clearly produced vowels exhibit longer duration and more extreme spectral properties than plain, conversational vowels. These features also characterize tense relative to lax vowels. This study explored the interaction of clear-speech and tensity effects by comparing clear and plain productions of three English tense-lax vowel pairs (/i-ɪ/, /ɑ-ʌ/, /u-ʊ/ in /kVd/ words). Both temporal and spectr...

We introduce spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. The associated integrable models (called integrable spin CalogeroMoser systems in the paper) and their Lax pairs are then obtained via Poisson reduction and gauge transformations. For Lie alg...

Abstract An extended Harry Dym hierarchy is constructed by using eigenfunctions and adjoint eigenfunctions of the spectral problems of the Harry Dym hierarchy associated with the pseudo-differential operator L = u∂ +u0 +u1∂−1 + · · ·. The corresponding Lax presentation possesses a self-consistent source involving squared eigenfunctions. The resulting extended Harry Dym hierarchy is reduced to t...

The paper investigates solutions and Lax pairs through bilinear Backlund transformations for some supersymmetric equations. We derive variety of from the known transformations. Besides, using gauge invariance (super) Hirota derivatives we may get deformed consequently with fermionic parameters. Examples are KdV equation KdV1 equation.

Lax pairs are useful in studying nonlinear partial differential equations, although finding them is often difficult. A standard approach for finding them was developed by Wahlquist and Estabrook [1]. It was designed to apply to for equations with two independent variables and generally produces incomplete Lie algebras (called “prolongation structures”), which can be written as relations among c...

Universal Lax pairs (the root type and the minimal type) are presented for CalogeroMoser models based on simply laced root systems, including E8. They exist with and without spectral parameter and they work for all of the four choices of potentials: the rational, trigonometric, hyperbolic and elliptic. For the elliptic potential, the discrete symmetries of the simply laced models, originating f...

This project investigates the articulatory properties of German vowels on the basis of tagged Cine-MRI data. German has 15 monophthongs, which are classified into seven tense-lax pairs. Understanding the phonetic correlate of vowel tenseness has proven elusive, partly due to the difficulty of obtaining global shape information for the tongue, especially the pharyngeal portion. Tagged Cine-MRI a...