{"product_id":"the-complex-wkb-method-for-nonlinear-equations-i-von-victor-p-maslov-ubersetzt-von-a-b-sossinsky-m-a-shishkova-m-a-shishkova-und-a-b-sossinsky","title":"The Complex WKB Method for Nonlinear Equations I","description":"\u003cp\u003eThis book deals with asymptotic solutions of linear and nonlinear equa­ tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)\/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ o. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp­ totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob­ lems of mathematical physics; certain specific formulas were obtained by differ­ ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter­ nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: \"One can hope that in the near future a computational pro­ cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783034896696\"\u003e\u003ch3\u003eLinear Theory\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783764350888\"\u003e\u003ch3\u003eLinear Theory\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783034896696","offer_id":49592334647621,"sku":"9783034896696","price":53.49,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783764350888","offer_id":49593006784837,"sku":"9783764350888","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/6902927c-0279-405e-b9df-099f68835e43.jpg?v=1772086157","url":"https:\/\/shop.autorenwelt.de\/products\/the-complex-wkb-method-for-nonlinear-equations-i-von-victor-p-maslov-ubersetzt-von-a-b-sossinsky-m-a-shishkova-m-a-shishkova-und-a-b-sossinsky","provider":"Autorenwelt Shop","version":"1.0","type":"link"}