Second-order solution of a nonlinear wave equation
Author:
R. W. Lardner
Journal:
Quart. Appl. Math. 39 (1981), 33-41
MSC:
Primary 35C20
DOI:
https://doi.org/10.1090/qam/613951
MathSciNet review:
613951
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Abstract: The method of multiple scales is used to investigate the nonlinear wave equation ${u_{tt}} - {u_{xx}} = \epsilon \left ( {2{u_x}{u_{xx}} - 2\lambda {u_t}} \right )$.
R. W. Lardner, The formation of shock waves in KBM solutions of hyperbolic differential equations, J. Sound & Vibr. 39, 489–502 (1975)
A. H. Nayfeh, Finite-amplitude longitudinal waves in non-uniform bars, J. Sound & Vibr. 42, 357–381 (1975)
- S. C. Chikwendu and J. Kevorkian, A perturbation method for hyperbolic equations with small nonlinearities, SIAM J. Appl. Math. 22 (1972), 235–258. MR 374635, DOI https://doi.org/10.1137/0122025
- Ali Hasan Nayfeh, Perturbation methods, John Wiley & Sons, New York-London-Sydney, 1973. Pure and Applied Mathematics. MR 0404788
- R. W. Lardner, Asymptotic solutions of nonlinear wave equations using the methods of averaging and two-timing, Quart. Appl. Math. 35 (1977/78), no. 2, 225–238. MR 442443, DOI https://doi.org/10.1090/S0033-569X-1977-0442443-5
- G. B. Whitham, Linear and nonlinear waves, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. MR 0483954
R. W. Lardner, The formation of shock waves in KBM solutions of hyperbolic differential equations, J. Sound & Vibr. 39, 489–502 (1975)
A. H. Nayfeh, Finite-amplitude longitudinal waves in non-uniform bars, J. Sound & Vibr. 42, 357–381 (1975)
S. C. Chikwendu and J. Kevorkian, A perturbation method for hyperbolic equations with small nonlinearities, SIAM J. Appl. Math. 22, 235–258 (1972)
A. H. Nayfeh, Perturbation methods, chap, vi (John Wiley, 1973)
R. W. Lardner, Asymptotic solutions of nonlinear wave equations using the methods of averaging and two-timing, Quart. Appl. Math. 35, 225–238 (1977)
G. B. Whitham, Linear and nonlinear waves, Wiley-Interscience, 1974, Sec. 2.7
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Article copyright:
© Copyright 1981
American Mathematical Society