| Autor: |
Schuurmans, M. F. H. |
| Zdroj: |
Journal of Engineering Mathematics; July 1971, Vol. 5 Issue: 3 p195-205, 11p |
| Abstrakt: |
Summary The validity of an approximation a0 of one of the solutions a of a set of two linear coupled dispersive wave equations has been discussed. a0 is the solution of a linear Korteweg-de Vries equation and satisfies the same initial condition as a. It is shown that for square integrable solutions having a spectral range not exceeding [-?, ?] the approximation is useful if ?5µ2t«1 in the sense that ?a-a0?(t)« ?a?(t)(L2-norm).µ is a measure for the dispersion. The approximation fails in that sense ast? 8. Some remarks to a similar nonlinear problem are made. |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
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