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We investigate a one-dimensional nonlinear wave system which arises from avariational principle modeling a type of cholesteric liquid crystals. Theproblem treated here is the Cauchy problem for the same wave speed case withinitial data on the parabolic degenerating line. By introducing a partialhodograph transformation, we establish the local existence of smooth solutionsin a weighted metric space based on the iteration method. A classical solutionof the primary problem is constructed by converting the solution in the partialhodograph variables to that in the original variables.

On the degenerate Cauchy problem for a nonlinear variational wave system, Part I: The same wave speed case