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Molotkov, I. A.; Vakulenko, S. A.

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).
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Cited in 5 Documents

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 soliton
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References:

[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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