Darboux System: Liouville Reduction and an Explicit Solution

R. Ch Kulaev, A. K. Pogrebkov, A. B. Shabat

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


For a Darboux system in ℝ3, we introduce a class of solutions for which an auxiliary second-order linear problem satisfies the factorization condition. We show that this reduction provides the (local) solvability of the Darboux system, and present an explicit solution to this problem for two types of dependent variables. We also construct explicit formulas for the Lamé coefficients and solutions to the associated linear problem. The previously known reduction to a weakly nonlinear system is shown to be a particular case of the approach proposed.

Original languageEnglish
Pages (from-to)250-269
Number of pages20
JournalProceedings of the Steklov Institute of Mathematics
Issue number1
Publication statusPublished - 1 Aug 2018


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