For each one of the Lie algebras gln and g̃ln, we constructed a family of integrable generalizations of the Toda chains characterized by two integers m+ and m−. The Lax matrices and the equations of motion are given explicitly, and the integrals of motion can be calculated in terms of the trace of powers of the Lax matrix L. For the case of m+ = m−, we find a symmetric reduction for each general...

We consider some natural connections which arise between right-flat (p, q) para-conformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a " Lax p-tuple " of linear differential operators, depending a spectral parameter which lives in (q − 1)-dimensional complex projective space. Generally, the differential operators contain partial derivatives ...

Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...

A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point complete integrability, is presented. Following procedure Ablowitz, Kaup, Newell and Segur (AKNS) we find that version Nonlinear Schrodinger equation, Hirota equation AKNS admit Lax pairs. We report each identified possesses Painleve property for partial differential admits t...

We study the deformations of the H equations, presented recently by Adler, Bobenko and Suris, which are naturally defined on a black-white lattice. For each one of these equations, two different three-leg forms are constructed, leading to two different discrete Toda type equations. Their multidimensional consistency leads to Bäcklund transformations relating different members of this class, as ...

Abstract. The class of nonlinear evolution equations (NLEE) – gauge equivalent to the N-wave equations related to the simple Lie algebra g are derived and analyzed. They are written in terms of S(x, t) ∈ g satisfying r = rank g nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov–Shabat dressing method is appropriately modified...

Several integrability tests for discrete equations will be reviewed. All tests considered can be applied directly to a given discrete equation and do not rely on the a priori knowledge of the existence of related structures such as Lax pairs. Specifically, singularity confinement, algebraic entropy, Nevanlinna theory, Diophantine integrability and discrete systems over finite fields will be des...

This paper explores the mapping of voice quality to affect, for a synthesised tense – lax voice continuum. Two questions are of interest. Firstly, over such a continuum, do listeners’ attributions of affect change in a continuous or in a more categorical way? Secondly, might discreetly different affects emerge at different points in the continuum: specifically, might a moderately tense voice cu...

The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with self-consistent sources. This offers a natural way to obtain the Lax representation for the mKPESCS. Based on the conjugate Lax pairs, we construct the generali...

The goal of this paper is twofold: to give a brief review of the latest research progress on electromagnetic modeling of vertical interconnects by using Foldy-Lax multiple scattering technique, to introduce a fast full-wave interconnect simulator, namely Foldy-Lax Via Tool, integrating all the extensions that recently have been made available. The kernel part of this novel approach is a mostly ...