On nonlinear waves in an elastic solid |
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| Institution: | 1. A.F. Ioffe Physical Technical Institute of the Russian Academy of Sciences, St. Petersburg, 194021 Russia;2. Instituto Pluridisciplinar, Universidad Complutense de Madrid, Paseo Juan XXIII, n° 1, Madrid 28040, Spain;1. Dipartimento di Scienze Matematiche “G. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy;2. Sector of Mathematical Physics, Lebedev Physical Institute of Russian Academy of Sciences, Leninskij Prospekt 53, 119991 Moscow, Russia;3. Department of Applied Mathematics, National Research Nuclear University MEPHI, Kashirskoe Shosse 31, 115409 Moscow, Russia;4. Department of Mechanics and Mathematics, Novosibirsk State University, 2 Pirogova street, 630090, Novosibirsk, Russia;1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;2. Department of Mathematics, Faculty of Science, King Faisal University, P.O. Box 400, Al-Ahsaa 31982, Saudi Arabia |
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| Abstract: | We describe the nonlinear dispersive dissipative evolution of strain waves in a solid in the limiting condition B∼O(R/L), where B is the characteristic amplitude of the wave, L its wavelength and R the radius of a solid rod. We also provide conditions on dissipation and dispersion for the propagation of either shocks or solitary waves of permanent form. |
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