Abstract
AbstractWe construct a reduction of the three-dimensional Darboux system for the Christoffel symbols, which describes orthogonal curvilinear coordinate systems. We show that the class of solutions of the Darboux system is parametrized by six functions of one variable (two for each of three independent variables). We give an explicit formulas for Darboux system solutions. In addition, we study the linear system associated with the Darboux system. This system reduces to a three-dimensional Goursat problem for a third-order equation with data on coordinate planes. It is shown that the solution to the Goursat problem admits the separation of variables and is determined by its values on the coordinate lines.KeywordsDarboux three-dimensional systemIntegrated systemGoursat problem with three variablesHydrodynamic type systemHamiltonian systemMathematics Subject Classification35L4037K15
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
