CONTENTS Introduction. Examples of non-standard characteristics. Statement of the general problem Chapter I. Characteristics of linear equations and equations with a non-local non-linearity § 1. Pseudodifferential operators with symbols and characteristics on arbitrary symplectic manifolds. Coordinate-momentum quantification conditions § 2. Electron terms § 3. Pseudodifferential operators with complex characteristics. Global asymptotic behaviour § 4. Problems in which there is a logarithmic asymptotic solution. The class of equations of tunnel type. The instanton as a logarithmic limit. Fourth generalization of the concept of characteristic § 5. Characteristics and global asymptotic behaviour as 
for equations with a non-local non-linearity. Equations of Vlasov type for wave front oscillation propagation. Bicharacteristics defining canonical transformations Chapter II. Characteristics of non-linear equations of general type § 1. Linear equations with rapidly oscillating coefficients. Non-linear wave equations having the equations of gas dynamics as characteristics. Equations of characteristics of composition of non-linear waves - equations of gas mixture dynamics § 2. The case of a weak quadratic and cubic non-linearity. Main resonances. Three- and four-train processes § 3. Propagation of singularities in non-linear equations. Conditions of Hugoniot type - the analogue of equations of characteristics for this problem. Singularities of branching type. Solutions with finite ejections at isolated points References
