ABSTRACT
This chapter is devoted to hyperbolic systems of hydrodynamic type. Equations of this type naturally arise in gasdynamics, hydrodynamics, chromatography, Whitham averaging procedure, etc. In this chapter, the authors briefly recall the main steps one usually has to follow when studying systems of this type. The general solution of the chromatography equations can be obtained by the generalized hodograph transform. Hence any semi-Hamiltonian system possesses an infinite number of first-order Lie–Bäcklund operators. In general it is not easy to solve the linear system. However, it is possible for some particular classes (e.g., weakly nonlinear systems, Temple systems, and so on).
