Darboux integrability of determinant and equations for principal minors

Dmitry K Demskoy, Dinh T Tran

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5 Citations (Scopus)
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We consider equations that represent a constancy condition for a 2D Wronskian, mixed Wronskian-Casoratian and 2D Casoratian. These determinantal equations are shown to have the number of independent integrals equal to their order-this implies Darboux integrability. On the other hand, the recurrent formulae for the leading principal minors are equivalent to the 2D Toda equation and its semi-discrete and lattice analogues with particular boundary conditions (cut-off constraints). This connection is used to obtain recurrent formulae and closed-form expressions for integrals of the Toda-type equations from the integrals of the determinantal equations. General solutions of the equations corresponding to vanishing determinants are given explicitly while, in the non-vanishing case, they are given in terms of solutions of ordinary linear equations.
Original languageEnglish
Pages (from-to)1973-1992
Number of pages20
Issue number7
Publication statusPublished - 2016


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