Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
- 1 May 1964
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 5 (5) , 611-613
- https://doi.org/10.1063/1.1704154
Abstract
In a recent paper Zabusky has given an accurate estimate of the time interval in which solutions of the nonlinear string equation ytt = c2(1 + εyx)yxx exist. A previous numerical study of solutions of this equation disclosed an anomaly in the partition of energy among the various modes; Zabusky's estimate shows that at the time when the anomaly was observed the solution does not exist. The proof of Zabusky uses the hodograph method; in this note we give a much simpler derivation of the same result based on an estimate given some years ago by the author.Keywords
This publication has 1 reference indexed in Scilit:
- Exact Solution for the Vibrations of a Nonlinear Continuous Model StringJournal of Mathematical Physics, 1962