Related papers: The semi-discrete AKNS system: Conservation laws, …
In this work, we propose a class of high order semi-Lagrangian scheme for a general consistent BGK model for inert gas mixtures. The proposed scheme not only fulfills indifferentiability principle, but also asymptotic preserving property,…
Formulated by Blesgen and Lowengrub and Truskinovsky, the `Navier-Stokes-Allen-Cahn' (NSAC) equations and the `Navier-Stokes-Cahn-Hilliard' (NSCH) equations describe diphasic fluid flow, combining the conservation laws for mass, momentum,…
We present a systematic procedure for obtaining the dispersionless limit of a class of N=1 supersymmetric systems starting from the Lax description of their dispersive counterparts. This is achieved by starting with an N=2 supersymmetric…
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant…
We describe a nonlinear kagome lattice with nonlinear dynamics described by Klein-Gordon interactions with a scalar unknown at each node, such as might occur in a nonlinear electrical lattice. We show that the dispersion relation has three…
The obstructions to the existence of a hierarchy of hydrodynamic conservation laws are studied for a multicomponent dispersionless KdV system. It is shown that if an underlying algebra is Jordan, then the lowest obstruction vanishes and…
The system of equations of one-dimensional shallow water over uneven bottom in Euler's and Lagrange's variables is considered. Intermediate system of equations is introduced. Hydrodynamic conservation laws of intermediate system of…
In this work, we present a semi-discrete scheme to approximate solutions to the scalar LWR traffic model with spatially discontinuous flux, described by the equation $u_t + (k(x)u(1-u))_x = 0$. This approach is based on the…
We consider an integrable generalization of the nonlinear Schr\"odinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS equation in the same way that the…
We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion…
We study a new example of equation obtained as a result of a recent generalized symmetry classification of differential-difference equations defined on five points of one-dimensional lattice. We have established that in the continuous limit…
KdV6 equation can be described as the Kupershmidt deformation of the KdV equation (see 2008, Phys. Lett. A 372: 263). In this paper, starting from the bi-Hamiltonian structure of the discrete integrable system, we propose a generalized…
We define a kinetic and a potential energy such that the principle of stationary action from Lagrangian mechanics yields a Camassa--Holm system (2CH) as the governing equations. After discretizing these energies, we use the same variational…
We construct an infinite hierarchy of nonlocal conservation laws for the $ABC$ equation $A u_t\,u_{xy}+B u_x\,u_{ty}+C u_y\,u_{tx} = 0$, where $A,B,C$ are constants and $A+B+C\neq 0$, using a nonisospectral Lax pair. As a byproduct, we…
Conservation laws are formulated for systems of differential equations by using symmetries and adjoint symmetries, and an application to systems of evolution equations is made, together with illustrative examples. The formulation does not…
The Ablowitz-Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localised solitons to rational solutions in the form of the spatiotemporally localised…
This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…
We study extremal shocks of $1$-d hyperbolic systems of conservation laws which fail to be genuinely nonlinear. More specifically, we consider either $1$- or $n$-shocks in characteristic fields which are either concave-convex or…
We study discrete vortices in the anti-continuum limit of the discrete two-dimensional nonlinear Schr{\"o}dinger (NLS) equations. The discrete vortices in the anti-continuum limit represent a finite set of excited nodes on a closed discrete…
We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the case of perturbation by the collision dynamic on the finite horizon $\mathbb Z$-periodic Lorentz gas and in view of…