Conservation Laws
“Irregularization” of systems of conservation laws
... of conservation laws (notably, those of hydrodynamics), the “proper” choice for solutions with defects turns out to be relatively tame, with defects consisting only of jump discontinuities and being ...
13
Explicit solutions and conservation laws of the logarithmic KP equation
... In this paper, we use the Lie group method to deal with (). The outline of the paper is as follows: In Section , the vectors fields are derived. In Section , symmetry reductions and explicit solutions are constructed. ...
11
Conservation laws for a generalized Ito-type coupled KdV system
... For variational problems, the celebrated Noether theorem [] provides an elegant way to construct conservation laws. In fact, it gives an explicit formula for determining a con- servation law once a ...
7
Self-adjointness, conservation laws and invariant solutions of the Buckmaster equation
... where U (t, x) is an arbitrary function. The solution ξ(t, x, U ) is the local multi- pliers of all non-trivial local conservation laws of zero-th order of the Buckmaster Eq. (5.4). Solving the above ...
14
Gauge-covariant extensions of Killing tensors and conservation laws
... This paper discusses symmetries and conservation laws in the context of hamiltonian dynamics. The discussion is framed predominantly in the language of classical dynamics, but the use of Poisson brackets ...
10
Semi Lagrangian Difference Approximations for Different Conservation Laws
... different conservation laws (of mass and kinetic energy) which are formulated in terms of the discrete norms similar to the L 1 and L 2 ...different conservation laws yield discrete ...
6
Error estimates for scalar conservation laws by a kinetic approach
... We use the kinetic approach of Perthame and Tadmor (1991) to calculate the error esti- mates for general scalar conservation laws governing problems in gas dynamics or fluid mechanics in general. The ...
15
Symmetries and conservation laws in non Hermitian field theories
... This is not true of the non-Hermitian theory. If we are to have δS = 0, and at the same time support non-trivial solutions (Φ 6 = 0), then at least one of the surface terms must yield a finite contribution. ...
20
From parametricity to conservation laws, via Noether's Theorem
... The use of invariance under change to derive useful conse- quences is a technique much older than programming languages. In physics, Noether’s theorem [14] provides a general way to derive conservation laws ...
12
Undercompressive shocks for scalar conservation laws with nonconvex fluxes
... In this section, we study numerical solutions of non-convex conservation laws with dif- fusion and dispersion. In the rst subsection, we illustrate the theoretical results of the previous section on the ...
26
The shallow water equations: conservation laws and symplectic geometry
... between conservation laws, nonsimple wave solutions and Bcklund transformations of both the homogenous and nonhomogenous systems... Perhaps we ought to call 3.2 the.[r] ...
6
A Role of the Conservation Laws in Evolutionary Processes and Generation of Physical Structures
... energy, linear momentum, angular momentum, and mass. They establish the balance between the variation of a phys- ical quantity and the corresponding external action. These are the conservation laws for ...
7
On the solutions and conservation laws of the coupled Drinfeld-Sokolov-Satsuma-Hirota system
... 22. Ibragimov, NH: CRC Handbook of Lie Group Analysis of Differential Equations, vol. I. CRC Press, Boca Raton (1993) 23. Ibragimov, NH: CRC Handbook of Lie Group Analysis of Differential Equations, vol. II. CRC Press, ...
11
Nonlinear conservation laws for the Schrödinger boundary value problems of second order
... As an application of the Phragmén–Lindelöf method related to a second-order bound- ary value problem with respect to the Schrödinger equation, in this paper we consider the conservation laws for a ...
14
A total variation diminishing high resolution scheme for nonlinear conservation laws
... Mathematical modeling of many problems in various fields of engineering such as fluid dynamics, aerodynamics, hydrodynamics, Magnetohydrodynamics (MHD),... lead to the nonlinear hyperbolic conservation laws ...
15
Numerical methods for conservation laws and related equations. Siddhartha Mishra
... Euler equations of gas dynamics. A gas (as an example consider air) con- sists of a large number of molecules. The motion of each molecule can be tracked individually. This description is termed as the particle ...
99
A moving mesh method for one-dimensional hyperbolic conservation laws
... conservation laws, that employs a high resolution Godunov-type scheme for the physical equations, in conjunctionwith a moving mesh PDE governing the motion of the spatial grid ...
23
Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity
... Undercompressive shocks were rst studied as solutions of nonstrictly hyperbolic sys- tems of conservation laws [7, 11, 14], and as special solutions of systems of mixed type [20, 12, 16, 18]. Recently ...
16
Multipliers : a general method of analysis for conservation laws of differential equations
... that this equation does not .have an infinite number of polynomial conservation laws or if it does they would be of a totally different form to those of the Korteweg-de Vries equation a [r] ...
186
An unfitted discontinuous Galerkin scheme for conservation laws on evolving surfaces
... Abstract. Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical ...
12