The equations that define the Lax pairs for generalized principal chiral models can be solved for any nondegenerate bilinear form on su(2). The solution is dependent on one free variable that can serve as the spectral parameter. 1 Formulation of the generalized chiral models Principal chiral models are important example of relativistically invariant field theory integrable by the inverse scatte...

In this paper, we construct a new integrable equation which is generalization of $q$-Toda equation. Meanwhile its soliton solutions are constructed to show property. Further the Lax pairs generalized and whole hierarchy also constructed. To integrability, Bi-hamiltonian structure tau symmetry given leads function.

This study examines the vowel-intrinsic fundamental frequency (IF0) for tense and lax vowels in German: These show a similar F0 but differ in their articulatory vowel height. This is contrary to commonly accepted biomechanical theories explaining IF0 by a physiological linkage between the upper vocal tract and the larynx. To examine this phenomenon, acoustic, electroglottographic and articulato...

A 3D full-wave approach, based on the Foldy-Lax multiple scattering equations, is successfully extended to model massivelycoupled multiple vias using differential signaling and shared antipad in high speed vertical interconnects. For the first time, this method has been used and tested on via-pair with shared antipad in multilayered structure. The magnetic frill current source on the port is ca...

<p style='text-indent:20px;'>We outline the construction of special functions in terms Fredholm determinants to solve boundary value problems string spectral problem. Our motivation is that problem related equations Lax pairs at least three nonlinear evolution from mathematical physics.</p>

A new set of discrete integrable equations, called face-centered quad was recently obtained using types interaction-round-a-face solutions the classical Yang-Baxter equation. These equations satisfy a formulation multidimensional consistency, known as consistency-around-a-face-centered-cube (CAFCC), which requires consistency an overdetermined system fourteen five-point on cubic unit cell. In t...

Given a pseudomonad $mathcal{T} $ on a $2$-category $mathfrak{B} $, if a right biadjoint $mathfrak{A}tomathfrak{B} $ has a lifting to the pseudoalgebras $mathfrak{A}tomathsf{Ps}textrm{-}mathcal{T}textrm{-}mathsf{Alg} $ then this lifting is also right biadjoint provided that $mathfrak{A} $ has codescent objects. In this paper, we give  general results on lifting of biadjoints. As a consequence, ...