Initial value problem of quasi-linear hyperbolic systems and global geometric optics approximation

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The aim of research :(1) Construction of formal solutions with the initial data involving a parametery lambda for quasi-linear symmetric strongly hyperbolic systems of partial differential equations(2) Verification of such formal solutions as globally valid weak formal solutions(3) Clarification of the relation of such weak global formal solutions and the genuine solution of the original systemsResults obtained through the present research :(1) 2-dimensionality of the range of the linear phase functions(2) Introduction of a minimal class of constituent functions for formal solutions(3) Tractable representaions of derived modultion equations using simplified phase parameters(4) Verification of a natural relation between weak solutions of derived modulation equations and weak formal solutions of the original systems in case of systems of conservation laws(5) Validity as weak formal solutions to the original systems of such global weak solutions of derived modulation equationsThe details will be expounded in papers in preparation which will be published elsewhere.