While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text.

The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians.

This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

In the introductory section, we review the formulation of the Korteweg-de Vries (KdV) equation and of the modified KdV (mKdV) equation as a compatibility condition for a Lax pair of linear operators.

... ( 1 ) part of the gauge group is necessary and plays important roles as in U ... soliton configuration and so on . Because of resolution of singularities , singular ... Integrable Systems NC extension of integrable equations such as the ...

... Soliton in the ( 2 + 1 ) -dimensional Nizhnik - Novikov - Veselov Equation ... solutions of the Nizhnik - Novikov- Veselov equation . Some exact solutions ... singular interactions : One is the resonant interaction that generates one line ...

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics.

... 1 , 1018-1031 ] . In this respect they are closer in nature to the small dispersion solutions to the KdV equation ... singular structures which can appear . By taking various limits - in which ... integrable systems theorists and more ...

The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas.