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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper develops two approaches to Lax-integrbale systems withspatiotemporally varying coefficients. A technique based on extended Lax Pairsis first considered to derive variable-coefficient generalizations of variousLax-integrable NLPDE hierarchies recently introduced in the literature. Asillustrative examples, we consider generalizations of the NLS and DNLSequations, as well as a PT-symmetric version of the NLS equation. It isdemonstrated that the techniques yield Lax- or S-integrable NLPDEs with bothtime- AND space-dependent coefficients which are thus more general than almostall cases considered earlier via other methods such as the Painleve Test, BellPolynomials, and various similarity methods. However, this technique, althoughoperationally effective, has the significant disadvantage that, for anyintegrable system with spatiotemporally varying coefficients, one must 'guess'a generaliza- tion of the structure of the known Lax Pair for the correspondingsystem with constant coefficients. Motivated by the somewhat arbitrary natureof the above procedure, we therefore next attempt to systematize the derivationof Lax-integrable sytems with variable coefficients. We attempt to apply theEstabrook- Wahlquist (EW) prolongation technique, a relatively self-consistentprocedure requiring little prior infomation. However, this immediately requiresthat the technique be significantly generalized or broadened in severaldifferent ways. The new and extended EW technique which results is illustratedby algorithmically deriving generalized Lax-integrable versions of NLS,PT-symmetric NLS, and DNLS equations.

Integrable Spatiotemporally Varying NLS, PT-Symmetric NLS, and DNLS Equations: Generalized Lax Pairs and Lie Algebras