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Two‐Wave Interactions for Weakly Nonlinear Hyperbolic Waves
Author(s) -
He Yuanping,
Moodie T. Bryant
Publication year - 1993
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1993883241
Subject(s) - nonlinear system , conservation law , perturbation (astronomy) , wave propagation , mathematical analysis , physics , classical mechanics , mathematics , hyperbolic partial differential equation , longitudinal wave , optics , quantum mechanics
This paper is devoted to studying the weakly nonlinear interaction of two waves whose propagation is governed by n × n hyperbolic systems of conservation laws. Our method of approach involves introducing two nonlinear phase variables and carrying out a perturbation analysis. This extended version of our previous single‐wave‐mode theory [5] is then applied to the equations of gas dynamics to study interacting sound waves. Numerical results for the wave‐wave interaction are presented graphically in a set of figures.