| Chromatographer is a physical chenfistry separate and analytical method,because it's provided with the characteristic of high efficiency, and fast speed,and better selectivity, and high delicacy, So it apply widely to science experiment and country economy and other fields. The key technique of nonlinear chromatography is the initial boundary value problem for nonlinear hyperbolic conservation laws systems. Because of the high nonlinear of the problem and the complexity of the described physics phenomenon, it is very significative to study them. In this paper, we research the initial-boundary value problem of the non-homogeneous hyperbolic conservation laws systems that A→B type nonlinear ideal reaction chromatography equations respectively. Firstly, According to the actual problem of the reaction chromatography, we establish the mathematics model of A→B type reaction chromatography. Secondly, aiming at the actual problem, by handling appropriately, the nonlinear ideal reaction chromatography equations are changed to two independence nonlinear hyperbolic conservation laws. According to the property of the characteristic line, and the necessary and sufficiency condition of the characteristics intersection and the constitution of base solution etc, We deduce detailed the expression of the solutions of the initial-boundary value problem of the non-homogeneous hyperbolic conservation laws systems that several types actual problem respectively, give the global solution including of the characteristic velocity of concentration wave, and the velocity of the shock wave, and the circulate time of the shock wave, and the elution curve etc.Finally, Take the wide pulse for example, ainfing at the difficulties of the concealed function and dynamic subsection function, using the Microsoft Office Excel 2003 and Origin Pro7.5 RSO software and MATLAB6.5,we give the corresponding arithmetic and get the numerical value simulate of the wave figure of elution curve.
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