The Asymptotic Solution of the Korteweg‐deVries Equation in the Absence of Solitons
- 1 February 1979
- journal article
- research article
- Published by Wiley in Studies in Applied Mathematics
- Vol. 60 (1) , 59-72
- https://doi.org/10.1002/sapm197960159
Abstract
The asymptotic solution of the Korteweg‐de Vries equation uτ + ⅓uxxx + 2uux = 0 for initial conditions from which no solitons evolve is obtained as a slowly varying similarity solution of the form τ−2/3(Vz−V2, where V = V(z/τ) and z = τ−1/3x. The results are consistent with, but go somewhat beyond, those recently obtained by Ablowitz and Segur [2] through a rather different approach.Keywords
This publication has 5 references indexed in Scilit:
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