{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T10:27:22Z","timestamp":1768732042928,"version":"3.49.0"},"reference-count":58,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,8]]},"abstract":"<jats:p> We present a variational formulation for the Kardar\u2013Parisi\u2013Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a potential we prove some global shift invariance properties previously conjectured by other authors. We also show a few results about the form of the stationary probability distribution function for arbitrary dimensions. The procedure used for KPZ was extended in order to derive more general forms of such a functional leading to other nonlinear kinetic equations, as well as cases with density dependent surface tension. <\/jats:p>","DOI":"10.1142\/s0218127409024505","type":"journal-article","created":{"date-parts":[[2009,11,3]],"date-time":"2009-11-03T11:10:49Z","timestamp":1257246649000},"page":"2813-2821","source":"Crossref","is-referenced-by-count":24,"title":["VARIATIONAL FORMULATION FOR THE KPZ AND RELATED KINETIC EQUATIONS"],"prefix":"10.1142","volume":"19","author":[{"given":"HORACIO S.","family":"WIO","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica de Cantabria, Universidad de Cantabria &amp; CSIC, E-39005 Santander, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.88.254101"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/3\/L01"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511599798"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(98)00622-7"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.59.5142"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/9\/4\/102"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.65.017105"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.65.851"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.75.031105"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01314255"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(01)00479-4"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.73.031104"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.70.223"},{"key":"rf14","volume-title":"Instabilities and Nonequilibrium Structures","author":"Graham R.","year":"1987"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.42.4661"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.76.4376"},{"key":"rf17","unstructured":"P.\u00a0H\u00e4nggi, Stochastic Processes Applied to Physics, eds. 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