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We construct a global conservative weak solution to the Cauchy problem forthe non-linear variational wave equation $v_{tt} - c(v)(c(v)v_x)_x +\frac{1}{2}(v+v^3)= 0$ where $c(\cdot)$ is any smooth function with uniformlypositive bounded value. This wave equation is derived from a wave systemmodelling nematic liquid crystals in a constant electric field.

Global Solution to a nonlinear wave equation of liquid crystal in the constant electric field