Burchnall–Chaundy_theory

Burchnall–Chaundy theory

Burchnall–Chaundy theory

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In mathematics, the Burchnall–Chaundy theory of commuting linear ordinary differential operators was introduced by Burchnall and Chaundy (1923, 1928, 1931).

One of the main results says that two commuting differential operators satisfy a non-trivial algebraic relation. The polynomial relating the two commuting differential operators is called the Burchnall–Chaundy polynomial.

References

  • Burchnall, J. L.; Chaundy, T. W. (1923), "Commutative ordinary differential operators", Proceedings of the London Mathematical Society, 21: 420–440, doi:10.1112/plms/s2-21.1.420, ISSN 0024-6115, S2CID 120180866
  • Burchnall, J. L.; Chaundy, T. W. (1928), "Commutative Ordinary Differential Operators", Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 118 (780), The Royal Society: 557–583, Bibcode:1928RSPSA.118..557B, doi:10.1098/rspa.1928.0069, ISSN 0950-1207, JSTOR 94922
  • Burchnall, J. L.; Chaundy, T. W. (1931), "Commutative Ordinary Differential Operators. II. The Identity Pn = Qm", Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 134 (824), The Royal Society: 471–485, Bibcode:1931RSPSA.134..471B, doi:10.1098/rspa.1931.0208, ISSN 0950-1207, JSTOR 95854
  • Gesztesy, Fritz; Holden, Helge (2003), Soliton equations and their algebro-geometric solutions. Vol. I (1+1)-dimensional continuous models, Cambridge Studies in Advanced Mathematics, vol. 79, Cambridge University Press, ISBN 978-0-521-75307-4, MR 1992536
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