Approximate solutions to nonlinear hyperbolic equations near diffractive points of arbitrary order are built as sums of incoming and reflected pulses whose phases and profiles satisfy transport equations in low-regularity high-frequency regimes.
Solving eikonal equations by the method of characteristics
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Propagation of nonlinear pulses near diffractive points of any order
Approximate solutions to nonlinear hyperbolic equations near diffractive points of arbitrary order are built as sums of incoming and reflected pulses whose phases and profiles satisfy transport equations in low-regularity high-frequency regimes.