An algebraic form of the factorization method

Author:

Stahlhofen A.,Bleuler K.

Publisher

Springer Science and Business Media LLC

Subject

General Medicine

Reference31 articles.

1. L. Infeld andT. E. Hull:Rev. Mod. Phys.,23, 21 (1951).

2. The roots of the factorization method can be traced back to Cauchy (1827). Detailed lists of references illustrating the history can be found inL. Schlesinger.Handbuch der Theorie der linearen Differentialgleichungen (Teubner, Leipzig, 1895), (According to Schlesinger, the first proof of factorizability of a general, linear differential equation of ordern apparently goes back to Frobenius.);E. L. Ince:Ordinary Differential Equations, 2nd ed. (Dover, 1956). (The relation between the factorization method and the theorem of Burchnall and Chaundy (cf. ref. (3) is shown in sect.5); The connection between the factorization method and the Riccati-equations is discussed in detail byDonald R. Smith:SIAM Rev.,29, 91 (1987).

3. J. L. Burchnall andT. W. Chaundy:Proc. London Math. Soc.,21, 420 (1923).

4. Since the amount of work dedicated to the factorization method and related topics is enormous, our list of references is by no means complete; we focus here on articles giving detailed lists of (earlier) references.

5. Applications of a higher-dimensional factorization method (in the form of the Darboux-transformation) to string theory is discussed byJ. Gamboa andJ. Zanelli:Ann. of Phys.,188, 239 (1988).

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