Symposium on Continuum Models and Discrete Systems (6th) Held in Dijon, France on June 26 - 29, 1989
Abstract
Based on Eringen's micromorphic theory of continua, new local balance laws, constitutive relations, field equations and an equation of state for bubbly liquids with single velocity and temperature fields have been recently developed. This paper considers the system of field equations which admits, in a linear approximation, a plane wave solution with high-frequency oscillation. For a wave of small but finite amplitude, we investigate how slowly varying parts of the wavetrain such as the amplitude are modulated by nonlinear interactions. The derivative-expansion method with multiple scales is applied to the analysis of weak nonlinear waves propagating through the mixture. Its shown that the nonlinear Schroedinger equation can be derived from the condition that the perturbation expansion be free from secular terms. For long waves, a stretching transformation shows that, in the lowest order of an asymptotic expansion, the original system of field equations of the mixture can be reduced to the Korteweg-de Vries equation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1986
- Accession Number
- ADA252319
Entities
Organizations
- Pierre and Marie Curie University