The classical generation theorem of conservation laws from known ones for a system of differential equations which uses the action of a canonical Lie–Bäcklund generator is extended to include any Lie–Bäcklund generator. Also, it is shown that the Lie algebra of Lie–Bäcklund symmetries of a conserved vector of a system is a subalgebra of the Lie–Bäcklund symmetries of the system. Moreover, we in...

Abstract In this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I -method (= method of almost conservation laws) to setting. As model example, consider defocusing cubic Schrödinger equation (SNLS) on $${\mathbb {R}}^3$$ R</mml:mr...

Discontinuities usually appear in solutions of nonlinear conservation laws even though the initial condition is smooth, which leads to great difficulty in computing these solutions numerically. The Runge-Kutta discontinuous Galerkin (RKDG) methods are efficientmethods for solving nonlinear conservation laws, which are highorder accurate and highly parallelizable, and can be easily used to handl...