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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Long time asymptotics of the Korteweg-de Vries equation
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by Stephanos Venakides PDF
Trans. Amer. Math. Soc. 293 (1986), 411-419 Request permission

Abstract:

We study the long time evolution of the solution to the Kortewegde Vries equation with initial data $\upsilon (x)$ which satisfy \[ \lim \limits _{x \to - \infty } \upsilon (x) = - 1,\qquad \lim \limits _{x \to + \infty } \upsilon (x) = 0\] 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.
References
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 293 (1986), 411-419
  • MSC: Primary 35B40; Secondary 35Q20
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0814929-0
  • MathSciNet review: 814929