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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Long time asymptotics of the Korteweg-de Vries equation


Author: Stephanos Venakides
Journal: Trans. Amer. Math. Soc. 293 (1986), 411-419
MSC: Primary 35B40; Secondary 35Q20
MathSciNet review: 814929
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Abstract: We study the long time evolution of the solution to the Kortewegde Vries equation with initial data $ \upsilon (x)$ which satisfy

$\displaystyle \lim \limits_{x \to - \infty } \upsilon (x) = - 1,\qquad \lim \limits_{x \to + \infty } \upsilon (x) = 0$

We show that as $ t \to \infty $ the step emits a wavetrain of solitons which asymptotically have twice the amplitude of the initial step. We derive a lower bound of the number of solitons separated at time $ t$ for $ t$ large.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0814929-0
PII: S 0002-9947(1986)0814929-0
Article copyright: © Copyright 1986 American Mathematical Society