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Almost integrable evolution equations

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Abstract

We present a 2-component equation with exactly two nontrivial generalized symmetries, a counterexample to Fokas' conjecture that equations with as many symmetries as components are integrable. Furthermore we prove the existence of infinitely many evolution equations with finitely many symmetries. We introduce the concept of almost integrability to describe the situation where one has a finite number of symmetries. The symbolic calculus of Gel'fand-Dikiî andp-adic analysis are used to prove our results.

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Authors and Affiliations

  1. Department of Mathematics, Vrije Universiteit Faculty of Sciences, De Boelelaan 1081A, Amsterdam, The Netherlands

    Peter H. van der Kamp

  2. Department of Mathematics, Vrije Universiteit Faculty of Sciences, De Boelelaan 1081A, Amsterdam, The Netherlands

    Jan A. Sanders

Authors
  1. Peter H. van der Kamp
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  2. Jan A. Sanders
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van der Kamp, P.H., Sanders, J.A. Almost integrable evolution equations. Selecta Mathematica, New Series 8, 705–719 (2002). https://doi.org/10.1007/BF02637315

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