{"product_id":"kdv-kam-von-thomas-kappeler-jurgen-poschel","title":"KdV \u0026 KAM","description":"\n                                \n                \u003cp\u003e\n                                        In this text the authors consider the Korteweg-de Vries (KdV) equation (u\n                    \n                    \u003csub\u003et\u003c\/sub\u003e\n                                         = - u\n                    \n                    \u003csub\u003exxx\u003c\/sub\u003e\n                                         + 6uu\n                    \n                    \u003csub\u003ex\u003c\/sub\u003e\n                                        ) 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.\n                \n                \u003c\/p\u003e\n                                \n                \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                                \n                \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                                \n                \n                \u003cp\u003eThe pertinent nondegeneracy conditions are verified by calculating the first few Birkhoff normal form terms -- an essentially elementary calculation. \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642056949\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783540022343\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642056949","offer_id":39435606982749,"sku":"9783642056949","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783540022343","offer_id":39617680146525,"sku":"9783540022343","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/86b75dba-7903-4c25-93ac-f7beffc23e41.jpg?v=1778216738","url":"https:\/\/shop.autorenwelt.de\/products\/kdv-kam-von-thomas-kappeler-jurgen-poschel","provider":"Autorenwelt Shop","version":"1.0","type":"link"}