Darboux Transformations In Integrable Systems: Theory And Their Applications To Geometry - Couverture rigide

Livre 3 sur 24: Mathematical Physics Studies

Gu, Chaohao; Hu, Anning; Zhou, Zixiang

 
9781402030871: Darboux Transformations In Integrable Systems: Theory And Their Applications To Geometry
Couverture rigide
ISBN 10 : 1402030878 ISBN 13 : 9781402030871
Editeur : Springer-Verlag New York Inc., 2004

Synopsis

GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such as solitary water wave, solitary signals in optical ?bre etc., and has many applications in science and technology (like optical signal communication). On the other hand, it gives many e?ective methods ofgetting explicit solutions of nonlinear partial di?erential equations. Therefore, it has attracted much attention from physicists as well as mathematicians. Nonlinearpartialdi?erentialequationsappearinmanyscienti?cpr- lems. Getting explicit solutions is usually a di?cult task. Only in c- tain special cases can the solutions be written down explicitly. However, for many soliton equations, people have found quite a few methods to get explicit solutions. The most famous ones are the inverse scattering method, B] acklund transformation etc.. The inverse scattering method is based on the spectral theory of ordinary di?erential equations. The Cauchyproblemofmanysolitonequationscanbetransformedtosolving a system of linear integral equations. Explicit solutions can be derived when the kernel of the integral equation is degenerate. The B] ac ] klund transformation gives a new solution from a known solution by solving a system of completely integrable partial di?erential equations. Some complicated "nonlinear superposition formula" arise to substitute the superposition principlein linear science.

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Éditeur
Springer-Verlag New York Inc.
Date d'édition
2004
Langue
anglais
ISBN 10 
1402030878
ISBN 13 
9781402030871
Reliure
Relié
Nombre de pages
308
Coordonnées du fabricant
KINESIS
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Autres éditions populaires du même titre

9789048167883: Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry

Edition présentée

ISBN 10 :  9048167884 ISBN 13 :  9789048167883
Editeur : Springer, 2010
Couverture souple