Nonlinear geometric optics with various frequencies for entropy solutions only in L∞ of multidimensional scalar conservation laws is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling, compactness, homogenization, and L–stability. New multidimensional features are recognized, especially including nonlinear propagations of oscilla...

In this paper we present a method of constructing discrete nonlinear accelerator lattice that has an approximate integral motion is given upfront. The under consideration Hamiltonian in normalized (canonical) coordinates preserved by with accuracy. We establish connection between the integrator and real lens arrangement. consider as analog computer apply known algorithms high-order symplectic i...