J S R Chisholm and A K Common 1987 J. Phys. A: Math. Gen. 20 5459 doi:10.1088/0305-4470/20/16/020
J S R Chisholm and A K Common
Show affiliationsA class of second-order nonlinear differential equations which arises in several branches of mathematical physics is considered. It is shown that equations of this class may be factorised into first-order equations of 'Riccati type'. Conditions are obtained, on the coefficient functions of the second-order equations, for the first-order equations to be of matrix Riccati form, whose solutions have a finite superposition property. The factorisation into first-order equations is then not unique, and there is an alternative first-order set of equations whose solutions do not have this superposition property. A second-order equation arising in the theory of pellet fusion processes is investigated in detail. Solutions are obtained when the corresponding first-order equations are of matrix Riccati from and shown to be equivalent to solutions derived by alternative methods. Lagrangian systems giving rise to equations of the class are also considered.
34A34 Nonlinear equations and systems, general
17Bxx Lie algebras and Lie superalgebras (For Lie groups, see 22Exx)
Issue 16 (11 November 1987)
J S R Chisholm and A K Common 1987 J. Phys. A: Math. Gen. 20 5459
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