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I am interested in literature on known wave solutions in continnum mechanics, precisely the following mechanical equation: $$\rho\partial_t^2u_i = C_{ijkl}\nabla_j\nabla_ku_{l}$$ My interest is spread around its study for cubic lattices, which doesn't seem straightforward to solve analytically to me. But I couldn't find a reference book or articles illustrating a peculiar solution of it.

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1 Answer 1

up vote 3 down vote accepted

Landau and Lifshitz, Theory of Elasticity, Course of Theoretical Physics, Vol 7 (1986) An older edition is available online here.

In my 3rd edition printing, the very same equation (well, with slightly different notation) is on page 92. In the online edition I referenced, check page 107.

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