Titlebook: Nonlinear Waves and Solitons on Contours and Closed Surfaces; Andrei Ludu Book 20071st edition Springer-Verlag Berlin Heidelberg 2007 Soli

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Mathematical Prerequisitesre solutions of nonlinear equations that could be partial differential (PDE), integrodifferential, finite difference-differential, or even functional equations. They describe the evolution of the wave solutions in space and time. These nonlinear equations are usually coupled with linear or nonlinear

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The Importance of the Boundary how is it possible to know the values of a function inside a compact domain, by knowing only its values on the boundary* Well, these simplifications are possible because the “bricks” are actually organized in complicated and versatile structures. For example the . algebras. And in addition, the com

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Vector Fields, Differential Forms, and Derivativesable down-to-earth textbook with theorems and demonstration confined in R.. Shifrin is also an excellent compact and shorter text with many applications. For more abstract treatment (I was always puzzled by a book about geometry which does not contain any figure in it, yet I appreciate its power of

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Motion of Curves and Solitons [46–48]. In many situations (e.g., when the inside bulk has the property of being “incompressible”) such contour representations are the most natural, and are simpler ones. Basically, the contour dynamics approach reduces the problem to the study of motion of curves and surfaces, especially the clo

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Kinematics of Hydrodynamicsurfaces, and fluid surfaces, and to compare their behavior in the Eulerian and Lagrangian frames. The following sections and chapters proceed on the assumption that the fluid is practically continuous and homogenous in structure. Of course, the concept of continuum is an abstraction that does not ta

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Nonlinear Surface Waves in One Dimension) equation for the shallow water long channel case, and its cnoidal waves and soliton solutions. Then we briefly present the MKdV equation and some nonlinear dispersion extension of it. In the last sections, we discuss some possible dynamical generalizations of the shallow water models on compact in

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Nonlinear Surface Waves in Two Dimensionspecial features of the compact three-dimensional flow but is simpler in calculations. In addition, it is not just an idealization, because there are systems that can be modeled with two-dimensional drop systems. Examples of such systems are highly flattened droplets in gravity moving frictionless on