Some physically relevant non-linear models with solitons, which have target space S 2 , are known to have submodels with infinitly many conservation laws defined by the eikonal equation. Here we calculate all the symmetries of these models and their submodels by the prolongation method. We find that for some models, like the Baby Skyrme model, the submodels have additional symmetries, whereas f...

We compute the length of geodesics on a Riemannian manifold by regular polynomial interpolation of the global solution of the eikonal equation related to the line element ds = gijdx dx of the manifold. Our algorithm approximates the length functional in arbitrarily strong Sobolev norms. Error estimates are obtained where the geometric information is used. It is pointed out how the algorithm can...

We present a new Fast Marching algorithm for a non-convex eikonal equation modeling front evolutions in the normal direction. The algorithm is an extension of the Fast Marching Method since the new scheme can deal with a time-dependent velocity without any restriction on its sign. We analyze the properties of the algorithm and we prove its convergence in the class of discontinuous viscosity sol...

The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereb...

In this paper we study an approximation scheme for a class of Hamilton-Jacobi problems for which uniqueness of the viscosity solution does not hold. This class includes the Eikonal equation arising in the Shape from Shading problem. We show that, if an appropriate stability condition is satissed, the scheme converges to the maximal viscosity solution of the problem. Furthermore we give an estim...

We investigate the limiting behavior of solutions to inhomogeneous $p$-Laplacian equation $-\Delta_p u = \mu_p$ subject Neumann boundary conditions. For right hand sides which are arbitrary signed measures we show that converge a Kantorovich potential associated with geodesic Wasserstein-$1$ distance. In regular case continuous characterize limit as viscosity solution an infinity Laplacian / ei...

Planckian scattering of particles with angular momenta is studied by describing them as sources of Kerr metric. In the shock wave formalism, it is found that the angular momenta do not contribute to the scattering amplitude in the eikonal limit. This is confirmed by using the wave equation of the test particle in the Kerr background. Typeset using REVTEX E-Mail: saurya,[email protected] 1

This contribution discusses the application of a fast and sloppy solution of the Eikonal equation – namely the dynamic distance potential field – for the simulation of the flow of a group of pedestrian agents through two bottlenecks with different capacity (width) but identical walking distance toward the destination. It is found that using the method leads to a better distribution of agents on...

This paper explores applications of the exponential splitting method for approximating highly oscillatory solutions of the n-dimensional paraxial Helmholtz equation. An eikonal transformation is introduced for oscillation-free platforms and matrix operator decompositions. It is found that the sequential, parallel and combined exponential splitting formulas possess not only anticipated algorithm...