Two‐Wave Interactions for Weakly Nonlinear Hyperbolic Waves | Zendy

He Yuanping | Zendy; Moodie T. Bryant | Zendy

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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.

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