In this paper, a model is derived to describe a quartic anharmonic interatomic interaction with an external potential involving a pair electron-phonon. The authors study the corresponding Cauchy Problem in the semilinear and quasilinear cases.
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Project supported by the Fundaçõao para a Ciencia e Tecnologia, Financiamento Base (Nos. 2008-ISFL-1-209, 2008-ISFL-1-297) and the Fundação para a Ciencia e Tecnologia Grant (No. PTDC/MAT/110613/2009).
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Dias, JP., Figueira, M. & Oliveira, F. On the Cauchy Problem describing an electron-phonon interaction. Chin. Ann. Math. Ser. B 32, 483–496 (2011). https://doi.org/10.1007/s11401-011-0663-2