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The Asymptotic Solution of the Korteweg‐deVries Equation in the Absence of Solitons
Author(s) -
Miles John W.
Publication year - 1979
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm197960159
Subject(s) - korteweg–de vries equation , mathematical physics , mathematics , similarity (geometry) , mathematical analysis , physics , quantum mechanics , nonlinear system , computer science , image (mathematics) , artificial intelligence
The asymptotic solution of the Korteweg‐de Vries equation u τ + ⅓ u xxx + 2 uu x = 0 for initial conditions from which no solitons evolve is obtained as a slowly varying similarity solution of the form τ −2/3 ( V z − V 2 , where V = V ( z/τ ) and z = τ −1/3 x . The results are consistent with, but go somewhat beyond, those recently obtained by Ablowitz and Segur [2] through a rather different approach.
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