Since the celebrated work by Lions, Papanicolaou and Varadhan in 1980’s, there has been a considerable attention to the homogenization problem for Hamilton-Jacobi equation: roughly speaking, how to describe what macroscopic properties and aspects of this equation survive, once all of its local features are neglected (for example, by averaging over faster and faster oscillations). The interest i...

We study the resurgent structure associated with a Hamilton Jacobi equation This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching We derive the Bridge equation which encompasses in nitely many resurgent relations satis ed by the formal solution and the other components of the formal integral

The first-arrival quasi-P wave travel-time field in an anisotropic elastic solid solves a first-order nonlinear partial differential equation, the qP eikonal equation, which is a stationary Hamilton–Jacobi equation. The solution of the paraxial quasi-P eikonal equation, an evolution Hamilton–Jacobi equation in depth, gives the first-arrival travel time along downward propagating rays. We devise...

We describe a non-perturbative method to solve the Hamilton-Jacobi equation for invariant surfaces in phase space. The problem is formulated in action-angle variables with a general nonlinear perturbation. The solution of the HamiltonJacobi equation is regarded as the fixed point of a map on the Fourier coefficients of the generating function. Periodicity of the generator in the independent var...

Abstract We study the homogenization of a Hamilton-Jacobi equation forced by rapidly oscillating noise that is colored in space and white time. It shown homogenized deterministic, and, general, has an enhancement effect, for which we provide quantitative estimate. As application, perform sensitivity analysis equations term with small amplitude, identify scaling at macroscopic effect felt. The r...