Related papers: Multi-Dimensional Conservation Laws and Integrable…
Some turbulent flows self-organize into large-scale structures, rather than breaking up into ever-smaller scales. Underpinning this phenomenon is the existence of two sign-definite quantities which are conserved by the dynamics.…
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…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
Two-dimensional reductions of the KP-Whitham system, namely the overdetermined Whitham modulation system for five dependent variables that describe the periodic solutions of the Kadomtsev-Petviashvili equation, are studied and…
The first example of the so-called "coupled" integrable hydrodynamic chain is presented. Infinitely many commuting flows are derived. Compatibility conditions of the first two of them lead to the remarkable Manakov--Santini system.…
Recent work giving a classification of kinematic and vorticity conservation laws of compressible fluid flow for barotropic equations of state (where pressure is a function only of the fluid density) in $n>1$ spatial dimensions is extended…
It is shown that invariants and relativistically invariant laws of conservation of physical quantities in Minkowski space follow from 4-tensors of the second rank, which are four-dimensional derivatives of 4-vectors, tensor products of…
We consider the nonlinear equations obtained from soliton equations by adding self-consistent sources. We demonstrate by using as an example the Kadomtsev-Petviashvili equation that such equations on periodic functions are not isospectral.…
Generalization of the modified KdV equation to a multi-component system, that is expressed by $(\partial u_i)/(\partial t) + 6 (\sum_{j,k=0}^{M-1} C_{jk} u_j u_k) (\partial u_i)/(\partial x) + (\partial^3 u_{i})/(\partial x^3) = 0, i=0, 1,…
We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments…
Subdiffusion is a generic feature of chaotic many-body dynamics with multipole conservation laws and subsystem symmetries. We numerically study this subdiffusive dynamics, using quantum automaton random unitary circuits, in a broad range of…
We describe a new method which allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a…
A long wave multi-dimensional approximation of shallow water waves is the bi-directional Benney-Luke equation. It yields the well-known Kadomtsev-Petviashvili equation in a quasi one-directional limit. A direct perturbation method is…
Using a nonlocal field transformation for the gauge field known as Cho--Faddeev--Niemi--Shabanov decomposition as well as ideas taken from generalized integrability, we derive a new family of infinitely many conserved currents in the…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
In this work we present new second order semi-discrete central schemes for systems of hyperbolic conservation laws on curvilinear grids. Our methods generalise the two-dimensional central-upwind schemes developed by Kurganov and Tadmor. In…
A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows with cylindrical…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
We present a new set of boundary conditions for General Relativity on AdS$_3$, where the dynamics of the boundary degrees of freedom are described by two independent left and right members of the Gardner hierarchy of integrable equations,…
A complete classification of integrable conservative hydrodynamic chains is presented. These hydrodynamic chains are written via special coordinates -- moments, such that right hand sides of these infinite component systems depend linearly…