English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The method of squared eigenfunction potentials (SEP) is developedsystematically to describe and gain new information aboutKadomtsev-Petviashvili (KP) hierarchy and its reductions. Interrelation to thetau-function method is discussed in detail. The principal result, which formsthe basis of our SEP method, is the proof that any eigenfunction of the generalKP hierarchy can be represented as a spectral integral over the Baker-Akhiezer(BA) wave function with a spectral density expressed in terms of SEP. In fact,the spectral representations of the (adjoint) BA functions can, in turn, beconsidered as defining equations for the KP hierarchy. The SEP method issubsequently used to show how the reduction of the full KP hierarchy to theconstrained KP hierarchies can be given entirely in terms of linear constraintequations on the pertinent tau-functions. The concept of SEP turns out to becrucial in providing a description of constrained KP hierarchies in thelanguage of universal Sato Grassmannian and finding the non-isospectralVirasoro symmetry generators acting on the underlying tau-functions. The SEPmethod is used to write down generalized binary Darboux-Backlundtransformations for constrained KP hierarchies whose orbits are shown tocorrespond to a new Toda model on a square lattice. As a result, we obtain aseries of new determinant solutions for the tau-functions generalizing theknown Wronskian (multi-soliton) solutions. Finally, applications to randommatrix models in condensed matter physics are briefly discussed.Comment: LaTeX, 30pgs, appendix added on binary Darboux-Backlund  transformation

Method of Squared Eigenfunction Potentials in Integrable Hierarchies of KP Type