By V. P. Maslov and G. A. Omel'yanov
The examine of asymptotic strategies to nonlinear platforms of partial differential equations is the most important device within the research of such structures and their purposes in physics, mechanics, and engineering. within the current e-book, the authors suggest a brand new strong approach to asymptotic research of suggestions, that are effectively utilized in terms of the so-called ""smoothed surprise waves"", i.e., nonlinear waves which range speedy in an area of front and slowly outdoors of this local. The proposed strategy, according to the examine of geometric gadgets linked to front, might be seen as a generalization of the geometric optics (or WKB) strategy for linear equations. This quantity bargains to a huge viewers an easy and obtainable presentation of this new approach. The authors current many examples originating from difficulties of hydrodynamics, nonlinear optics, plasma physics, mechanics of continuum, and thought of section transitions (problems of unfastened boundary). within the examples, characterised by way of smoothing of singularities as a result of dispersion or diffusion, asymptotic suggestions within the type of distorted solitons, kinks, breathers, or smoothed surprise waves are built. through a unified rule, a geometrical photo is linked to each one actual challenge that permits for acquiring tractable asymptotic formulation and offers a geometrical interpretation of the actual approach. incorporated are many figures illustrating many of the actual results.