The notion of solitons arose with the study of partial differential equations at the end of the 19th century in more recent times their study has involved ideas from other areas of mathematics such as algebraic gometry topology and in particular infinite dimensional lie algebras and it this approach that is the main theme of this bookthis book will be of great interest to all whose . Solitons differential equations symmetries and infinite dimensional algebras this book investigates the high degree of symmetry that lies hidden in integrable systems. Solitons differential equations symmetries and infinite dimensional algebras cambridge tracts 1999. To that end differential equations arising from classical mechanics such as the kdv equation and the kp equations are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable systems. Cal mechanics nonlinear differential equations arising in the differential geometry of surfaces the study of commutative subrings of rings of dif ferential operators and so on
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