Darboux System: Liouville Reduction and an Explicit Solution View Full Text


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Article Info

DATE

2018-08

AUTHORS

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

ABSTRACT

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. More... »

PAGES

250-269

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s0081543818060123

DOI

http://dx.doi.org/10.1134/s0081543818060123

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111104692


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