Questions About Elastic Waves by Jüri Engelbrecht

Author:Jüri Engelbrecht
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(6.20)

The Cole-Hopf transformation (6.7) for the Burgers equation,

(6.21)

is modified [90] to

(6.22)

which can be written in the form of the Schrödinger equation

(6.23)

The wave profile u(r, ξ), where r is a parameter, now represents a scattering potential in (6.23). Therefore, we have to solve

(6.24)

where u 0(ξ) is the initial condition, and determine the discrete eigenvalues κ n , the normalization coefficients c n (0) and the reflection coefficients b(λ). Hence, the problem is reduced to solving the Gelfand-Levitan equation:

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