Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs.
Equations of Fluid dynamics and the shallow water approximation.- Integrability and related analytical properties of nonlinear PDE systems.- Analytical properties of some classical shallow-water models.- Discussion.
“This book can serve as an invaluable reference for anyone interested in the integrability properties of nonlinear partial differential equations, particularly those of the ‘wave type’ category.” (Adrian Muntean, Mathematical Reviews, April, 2025)