For a hyperbolic system of conservation laws, in fact a model for electrophoretic separation of \(n\) species of ions, is established a one- to-one correspondence between the weak solutions of the given equations and pairs of functions, meaning separation, uncoupling of linear modes and the nonlinear modes of the given system. It is utilized a linear change as in C. M. Dafermos and X. Geng [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 8, No. 3/4, 231-269 (1991; Zbl 0776.35033)].