2004, ISBN: 9781402030871

[ED: Gebunden], [PU: Springer Netherland], GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing i… Meer...

[ED: Gebunden], [PU: Springer Netherland], 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..., DE, [SC: 0.00], Neuware, gewerbliches Angebot, 310, [GW: 619g], Banküberweisung, PayPal, Sofortüberweisung<

2004, ISBN: 9781402030871

[ED: Gebunden], [PU: Springer Netherland], GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing i… Meer...

[ED: Gebunden], [PU: Springer Netherland], 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..., DE, [SC: 0.00], Neuware, gewerbliches Angebot, 310, [GW: 619g], Banküberweisung, PayPal, Sofortüberweisung<

ISBN: 9781402030871

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play… Meer...

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry. This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years. Audience: The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics., Springer<

ISBN: 9781402030871

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play… Meer...

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry.This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years. New Textbooks>Hardcover>Science>Mathematics>Mathematics, Springer Netherlands Core >2 >T<

ISBN: 9781402030871

Hardback, [PU: Springer-Verlag New York Inc.], Presents the Darboux transformations in matrix form and provides algebraic algorithms for constructing the explicit solutions. This work elu… Meer...

Hardback, [PU: Springer-Verlag New York Inc.], Presents the Darboux transformations in matrix form and provides algebraic algorithms for constructing the explicit solutions. This work elucidates the behavior of simple and multi-solutions, even in multi-dimensional cases. It contains many results that were obtained by the authors in the past few years., Physics<