{"product_id":"9783642056949","title":"Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge \/ A Series of Modern Surveys in Mathematics","description":"\u003ch1\u003eErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge \/ A Series of Modern Surveys in Mathematics\u003c\/h1\u003e \u003ch2\u003eKappeler, Thomas; Pöschel, Jürgen\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn this text the authors consider the Korteweg-de Vries (KdV) equation (u\u003csub\u003et\u003c\/sub\u003e = - u\u003csub\u003exxx\u003c\/sub\u003e + 6uu\u003csub\u003ex\u003c\/sub\u003e) with periodic boundary conditions. Derived to describe long surface waves in a narrow and shallow channel, this equation in fact models waves in homogeneous, weakly nonlinear and weakly dispersive media in general.\u003c\/p\u003e\n\u003cp\u003eViewing the KdV equation as an infinite dimensional, and in fact integrable Hamiltonian system, we first construct action-angle coordinates which turn out to be globally defined. They make evident that all solutions of the periodic KdV equation are periodic, quasi-periodic or almost-periodic in time. Also, their construction leads to some new results along the way. \u003c\/p\u003e\n\u003cp\u003eSubsequently, these coordinates allow us to apply a general KAM theorem for a class of integrable Hamiltonian pde's, proving that large families of periodic and quasi-periodic solutions persist under sufficiently small Hamiltonian perturbations. \u003c\/p\u003e\n\u003cp\u003eThe pertinent nondegeneracy conditions are verified by calculating the first few Birkhoff normal form terms -- an essentially elementary calculation. \u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2010-10-19\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783642056949\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-662-08054-2\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 279\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44343407411340,"sku":"9783642056949","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783642056949.jpg?v=1779040805","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783642056949","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}