Wronskian

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Wronskian

[′vrän·skē·ən]

(mathematics)

An n × n matrix whose i th row is a list of the (i - 1)st derivatives of a set of functions f₁, …, f_n; ordinarily used to determine linear independence of solutions of linear homogeneous differential equations.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Wronskian

a functional determinant composed of n functions f₁(x), f₂(x)....,f_n(x) and their derivatives up to the order n - 1 inclusive:

The vanishment of the Wrońskian [W(x) = 0] is a necessary and, under certain additional assumptions, a sufficient condition for the linear dependence between the given n functions, differentiated n - 1 times. Based on this, the Wrońskian is used in the theory of linear differential equations. The Wrońskian was introduced by J. Wroński in 1812.

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References in periodicals archive ?

Many methods have been developed to find the explicit solutions of nonlinear evolution equations; example of such methods are the first integral method [9], Jacobi elliptic function method [10], Hirota bilinear method [11], Wronskian determinant technique [12], F-expansion method [13], Darboux Transformations [14], Backlund transformation method [6], Miura transformation [15], homotopy perturbation method [16], and Adomian decomposition method [17].

Explicit Solutions to the (3+1)-Dimensional Kudryashov-Sinelshchikov Equations in Bubbly Flow Dynamics

By expanding the Wronskian determinant W[[f.sub.1], [f.sub.2],..., [f.sub.n]] with respect to the first row, we obtain

An extension of ABC-theorem (1)

had introduced the matrix element in Wronskian determinants when they used the Wronskian technique to solve soliton equations [19-23].