  In this paper, we study the bilinear form and the general N-soliton solution
for a two-component Hunter-Saxton (2-HS) equation, which is the short wave
limit of a twocomponent Camassa-Holm equation. By defining a hodograph
transformation based on a conservation law and appropriate dependent variable
transformations, we propose a set of bilinear equations which yields the 2-HS
equation. Furthermore, we construct the N-soliton solution to the 2-HS equation
based on the tau functions of an extended two-dimensional Toda-lattice
hierarchy through reductions. One- and two-soliton solutions are calculated and
analyzed.
