ASYMPTOTIC SOLUTION OF A DISPERSIVE HYPERBOLIC EQUATION WITH VARIABLE COEFFICIENTS.
NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
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Initial-boundary value problems are considered for an energy conserving dispersive hyperbolic equation, the Klein-Gordon equation. This equation contains the main feature of dispersion The speed of propagation depends on the frequency. The asymptotic expansion of solutions obtained by a technique which we call the ray method is compared with the asymptotic expansion of the exact solution. In every case considered, the solutions agree. Solutions are obtained for a series of initial-boundary value problems in one space dimension with variable coefficients. A new feature which is called space-time diffraction is found. This phenomenon has the following physical interpretation A portion of the energy of a wave reaches a boundary surface and then gradually leaks off, leaving a diminishing residue on the boundary for all time. Author