Burchnall–Chaundy theory

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 
• 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, The Royal Society, 118 (780): 557–583, 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 = Q^m", Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, The Royal Society, 134 (824): 471–485, 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, 79, Cambridge University Press, ISBN 978-0-521-75307-4, MR 1992536