Nonlinear longitudinal waves in inhomogeneous rods. (English. Russian original) Zbl 0486.73056
J. Sov. Math. 20, 2434-2441 (1982); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 99, 64-73 (1980).
MSC:
74H45 | Vibrations in dynamical problems in solid mechanics |
35Q99 | Partial differential equations of mathematical physics and other areas of application |
74J20 | Wave scattering in solid mechanics |
74E05 | Inhomogeneity in solid mechanics |
74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
35B20 | Perturbations in context of PDEs |
Keywords:
longitudinal vibrations of rod; nonlinear and dispersion effects; effects caused by inhomogeneity; perturbed Korteweg-de Vries equation; development of perturbation method; Cauchy problem; deformation of solitonReferences:
[1] | L. A. Ostrovskii and A. M. Sutin, ?Nonlinear elastic waves in rods,? Prikl. Mat. Mekh.,41, No. 3, 531?537 (1977). · Zbl 0392.73030 |
[2] | D. J. Kaup, ?A perturbation expansion for the Zakharov-Shabat inverse scattering transform,? SIAM J. Appl. Math.,31, 121?133 (1976). · Zbl 0334.47006 · doi:10.1137/0131013 |
[3] | V. I. Karpman and E. M. Maslov, ?On perturbation theory for solitons,? Zh. Eksp. Teor. Fiz.,73, No. 2(8), 537?558 (1977). |
[4] | V. I. Karpman and E. M. Ma-slov, ?The structure of tails formed by perturbation of solitons,? Zh. Eksp. Teor. Fiz.,75, No. 2(8), 504?517 (1978). |
[5] | S. A. Vakulenko, {C The effect of perturbation on the solitons of some nonlinear equations,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,89, 91?96 (1979). |
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