A level set algorithm for tracking discontinuities in hyperbolic conservation laws is presented. The algorithm uses a simple finite difference approach, analogous to the method of lines scheme presented in [20]. The zero of a level set function is used to specify the location of the discontinuity. Since a level set function is used to describe the front location, no extra data structures are ne...

This artic!e considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. _Veighted residual approxim...

The nonlinear stability in the //-norm, p > 1 , of stationary weak discrete shocks for the Lax-Friedrichs scheme approximating general m x m systems of nonlinear hyperbolic conservation laws is proved, provided that the summations of the initial perturbations equal zero. The result is proved by using both a weighted estimate and characteristic energy method based on the internal structures of t...

Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to ...

The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general method include equations on quantum plane, supersymmetric equations for chiral and antichiral supermultiplets as well as auxiliary equations of integrable model...

The convergence of the vanishing viscosity method for initialboundary value problems is analyzed for nonlinear hyperbolic conservation laws through several representative systems. Some techniques are developed to construct the global viscous solutions and establish the H−1 compactness of entropy dissipation measures for the convergence of the viscous solutions with general initial-boundary cond...

A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and scattering data with suitable symmetries are discussed. A method to find pure soliton solutions is given. An explicit breathing one soliton solution is found. Key properties are discussed and contras...

*Correspondence: [email protected] 1College of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P.R. China Full list of author information is available at the end of the article Abstract The symmetry analysis method is used to study the Drinfeld-Sokolov-Wilson system. The Lie point symmetries of this system are obtained. An optimal system of one-dimensional subalgebras ...

We show that if performance measures in stochastic and dynamic scheduling problems satisfy generalized conservation laws, then the feasible space of achievable performance is a polyhedron called an extended polymatroid that generalizes the usual polymatroids introduced by Edmonds. Optimization of a linear objective over an extended polymatroid is solved by an adaptive greedy algorithm, which le...

Abstract In this paper, a Lie symmetry method is used for the nonlinear generalized Camassa–Holm equation and as result reduction of order computing conservation laws are presented. Furthermore, μ -symmetry -conservation obtained.