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On the Kaup-Kupershmidt equation. Completeness relations for the squared solutions. (English) Zbl 1193.35200
Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 308-319 (2008).
Summary: We regard a cubic spectral problem associated with the Kaup-Kupershmidt equation. For this spectral problem we prove a completeness of its “squared” solutions and derive the completeness relations which they satisfy. The spectral problem under consideration can be naturally viewed as a 3 -reduced Zakharov-Shabat problem related to the algebra 𝔰𝔩(3,). This observation is crucial for our considerations.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
22E70Applications of Lie groups to physics; explicit representations
37K30Relations of infinite-dimensional systems with algebraic structures
35P05General topics in linear spectral theory of PDE