Microstructured Materials: Inverse Problems by Jaan Janno & Jüri Engelbrecht

Author:Jaan Janno & Jüri Engelbrecht
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(6.29)

Observing that the relation is valid between the inverses of non-canonical and canonical solutions, by Theorem 6.2 we see that the asymmetry on the relative level y has the formula

(6.30)

Therefore, the asymmetry depends on the velocity, the coefficients of linear terms b, β, γ, and on the ratio of the coefficients of nonlinear terms in micro- and macroscale . The nonlinearity coefficients μ and λ have different impact to the wave process. The nonlinearity in macroscale, i.e., μ balances the dispersion and opens the possibility for the solitary wave. But the nonlinearity in microscale, i.e., λ disturbs this balance. The ratio affects the shape of the wave. The bigger is the quantity , the bigger is the asymmetry. The balance between nonlinearity and dispersion collapses at the value

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