A Comparison of Perturbation Methods for Nonlinear Hyperbolic Waves

摘要: Publisher Summary This chapter discusses the comparison of perturbation methods for nonlinear hyperbolic waves. It five numbers including method renormalization, strained coordinates, analytic characteristics, multiple scales, and Krylov–Bogoliubov–Mitropolsky method. These techniques are applied to acoustic waves propagating in thermoviscous fluids. For lossless, oppositely traveling, one-dimensional waves, a first-order uniformly valid expansion can be obtained by using any these provided do not mutually interact body medium. is so if periodic or pulses. If mutual-interaction terms negligible, only characteristics used. dissipative media, it clear how one use determine an approximate solution when dissipation term same order as term. conservative multidimensional combination renormalization matched asymptotic expansions appear most powerful. In applying multi-dimensional obtain characteristic surfaces chosen appropriately. that short compared with radii curvature wave fronts, choosing appropriate does present difficulty because linear displays role geometric rays.