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.
An investigation of the myth, history, inscriptions, architecture, sculpture, painting, iconological program, festival, rituals and theater of the only known intact ancient dragon king temple in China
Sea area reclamation is one important activity where land is obtained in coastal countries and regions. It is also a marine development activity with great environment impact. Management technologies for sea area reclamation is the technologies system for sea area reclamation management.This compendium is a summary of the research and application of reclamation management technology in China. It makes a thorough study and systematic exposition of the main technical links of reclamation management.This comprehensive reference text provides a window for domestic and abroad reclamation managers, reclamation demonstration and assessment workers, reclamation project owners and even teachers and students keen in reclamation management.
Signal transduction is one of the most exciting research areas in modern biology as it deals with how information flows from the extracellular environment into a living cell to change its metabolism, genotype and phenotype. With the completion of the genomes of human and several other species, it becomes even more important to elucidate the molecul
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