Excerpt from Asymptotic Solution of a Dispersive Hyperbolic Equation With Variable Coefficients In the past few years there has been a great deal of interest in the asymptotic expansion of solutions of boundary value problems and initial boundary value problems for partial differential equations. These expansions are obtained for large distance and/or time or for large values of a parameter which may appear naturally in the equation and/or initial conditions, boundary conditions, etc. Many of these problems can be treated ...
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Excerpt from Asymptotic Solution of a Dispersive Hyperbolic Equation With Variable Coefficients In the past few years there has been a great deal of interest in the asymptotic expansion of solutions of boundary value problems and initial boundary value problems for partial differential equations. These expansions are obtained for large distance and/or time or for large values of a parameter which may appear naturally in the equation and/or initial conditions, boundary conditions, etc. Many of these problems can be treated by a method in which special curves, called rays, in space or space-time plan an essential role. The asymptotic solution is determined in terms of amplitude and phase functions which satis fy ordinary differential equations on these rays. These equations can often be solved explicitly, so that the solution to the original problem is known if the initial values on the rays of the amplitude and phase functions are known. In some cases these initial values can be determined directly from the data initial conditions, boundary conditions, etc.) of the given problem, while in other situations an indirect method is necessary. This method involves the exact solution of a canonical problem i.a., a problem simpler than that given originally but having the same local features as the given problem. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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