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AN INTRODUCTION TO NONLINEAR HYPERBOLIC WAVESA Wave Equation with Genuine NonlinearityBreakdown of a Genuine SolutionConservation Law and Jump ConditionStability Consideration, Entropy Condition, and ShocksSome ExamplesShock Structure, Dissipation and Entropy ConditionThe Persistence of a ShockNonlinear Wavefront and Shock FrontHopf's Result on the General SolutionEqual Area Rule for Shock FittingHYPERBOLIC SYSTEM-SOME BASIC RESULTSHyperbolic System of First Order Equations in Two Independent VariablesThe Wave Equation in m(>1) Space DimensionsHyperbolic System in More than Two Independent VariablesBicharacteristic Curves, Rays, and Compatibility ConditionPropagation of Discontinuities of First Order Derivatives Along RaysSIMPLE WAVE, HIGH FREQUENCY APPROXIMATION, AND RAY THEORYSimple WaveHigh-Frequency Approximation, Wavefront, Huygens' Method and Fermat's PrincipleKinematics of a Propagating CurveBreakdown of the Continuity of a Solution of a Quasilinear SystemJump Conditions for a Curved ShockWEAKLY NONLINEAR RAY THEORY (WNLRT) DERIVATIONA Historical AccountDerivation of CPW TheoryA Geometric Derivation of WNLRTAn Asymptotic Derivation of WNLRTSTABILITY OF SOLUTIONS NEAR A SINGULARITY OF SONIC TYPEIntroductionOne-Dimensional Weakly Nonlinear Wave PropagationWaves in a Multi-Dimensional Steady Transonic FlowWNLRT IN A POLYTROPIC GASBasic EquationsGeometrical Features of a Nonlinear WavefrontExact Solution of an Initial Value ProblemConclusion and Validity of WNLRTCOMPATIBILITY CONDITIONS ON A SHOCK: SINGLE CONSERVATION LAWDerivation of the Infinite System of Compatibility ConditionsExistence and Uniqueness of the Solution of the Infinite SystemA New Theory of Shock Dynamics: Analytic ConsiderationsA New Theory of Shock Dynamics: Comparison of Numerical Results with the Exact SolutionConclusionONE-DIMENSIONAL PISTON PROBLEM: AN APPLICATION OF NTSDFormulation of the ProblemDynamical Compatibility ConditionsInitial Conditions for the Piston ProblemResults and Discussions COMPATIBILITY CONDITIONS ON A MULTI-DIMENSIONAL SHOCKShock RaysShock Manifold Equation for a Weak ShockGeometrical and Kinematical Compatibility ConditionsDynamical Compatibility ConditionsA Weak Shock Ray TheoryPROPAGATION OF A CURVED WEAK SHOCKGoverning Equations of the NTSDConservation Form of the Equations for a 2-Dimensional Shock PropagationInitial Conditions, Results, and DiscussionComparison with other TheoriesCorrugational Stability and Persistence of a Kink