Konopelchenko-Dubrovsky方程组的对称,精确解和守恒律

通过利用修正的CK直接方法,建立了Konopelchenko-Dubrovsky（KD）方程组的新旧解之间的关系．利用李群分析方法,得到了（2＋1）维KD方程的对称、相似约化和新的精确解,包括指数函数解、双曲函数解、和三角函数解．同时找到了此方程的无穷多守恒律．     

Exact solutions and conservation laws in dissipative fluid dynamics

In this paper the 1D Euler system with a source term is considered in the case of isentropic flows. Classes of exact solutions of the equations under interest have been determined within the framework of the differential constraint method and a Riemann problem was solved. Finally Conservation Laws of the system here considered have been determined following the Direct Method.

     

Nonlocal symmetries,exact solutions and conservation laws of the coupled Hirota equations

Using the Lax pair, nonlocal symmetries of the coupled Hirota equations are obtained. By introducing an appropriate auxiliary dependent variable, the nonlocal symmetries are successfully localized to Lie point symmetries. With the help of Lie symmetries of the closed prolongation, exact solutions and nonlocal conservation laws of the coupled Hirota equations are studied.     

A method for computing symmetries and conservation laws of integra-differential equations

A method for computing symmetries and conservation laws of integro-differential equations is proposed. It resides in reducing an integro-differential equation to a system of boundary differential equations and in computing symmetries and conservation laws of this system. A geometry of boundary differential equations is constructed like the differential case. Results of the computation for the Smoluchowski's coagulation equation are given.     

On conservation laws for hyperbolized equations

We carry out an analysis of hyperbolized equations of diffusion type convenient for modeling on high-performance computer systems; in particular, we study conservation laws for these equations.     

Exact solutions and conservation laws of Zakharov-Kuznetsov modified equal width equation with power law nonlinearity

This paper obtains solutions to the Zakharov-Kuznetsov modified equal width equation with power law nonlinearity. The Lie symmetry approach and the simplest equation method are used to obtain these solutions. Moreover, conservation laws are derived for the underlying equation by employing two approaches: the new conservation theorem and the multiplier method.     

Exact solutions ofG-invariant chiral equations

A method is suggested for solving the chiral equations (αg,zg ⁻¹),ˉz+(αg,ˉzg ⁻¹),z=0, whereg belongs to some Lie groupG. The solution is written out in terms of harmonic maps. The method can be used even for some infinite-dimensional Lie groups. Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 710–716, November, 1995. The work was supported in part by the foundation CONACyT-México.     

Exact controllability to trajectories for entropy solutions to scalar conservation laws in several space dimensions

We describe a new method that 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 natural geometric condition.     

Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.     

Symmetries and conservation laws of Kadomtsev-Pogutse equations

Kadomtsev-Pogutse equations are of great interest from the viewpoint of the theory of symmetries and conservation laws and, in particular, enable us to demonstrate their potentials in action. This paper presents, firstly, the results of computations of symmetries and conservation laws for these equations and the methods of obtaining these results. Apparently, all the local symmetries and conservation laws admitted by the considered equations are exhausted by those enumerated in this paper. Secondly, we point out some reductions of Kadomtsev-Pogutse equations to more simpler forms which have less independent variables and which, in some cases, allow us to construct exact solutions. Finally, the technique of solution deformation by symmetries and their physical interpretation are demonstrated.     

Symmetries and conservation laws of difference equations

Within the formalism of difference jets, we develop an algebro-geometric analysis of systems of difference equations on multidimensional integer lattices and study their symmetries and conservation laws.     

Regularity of solutions to the perturbed conservation laws

A kind of regularity for the mild solution of perturbed conservation laws is proposed. This regularity is described in term of variations measured in the L¹-norm. A dissipativity condition from the semigroup approach is used to show that the mild solution stays within a class of bounded variation in this sense of regularity. This shows that this class of functions is an invariant of the semigroup. The same analysis carries over to the periodic problem. The class of boundedL¹-variation functions used here can be normed to give a Banach space structure. It also has an analogue with the space of Lipschitz functions     

Exact solutions using symmetry methods and conservation laws for the viscous flow through expanding–contracting channels

We present a range of definitions and methods dealing with the reduction of partial differential equations on the basis of the underlying symmetry structure, conservation laws and a combination of these. The method is used to reduce a complex system to an easy-to-handle second-order ordinary differential equation system independent of restrictions on any physical parameters. In particular, we construct exact solutions of a system modelling viscous flow between slowly expanding and contracting walls.     

Third-order scalar evolution equations with conservation laws

Associated to the family of third-order quasilinear scalar evolution equations is the geometry of point transformations. This geometry provides a framework from which to study the structure of conservation laws of the equation, and to study the special nature of the geometry of those equations which do possess conservation laws. There is an easy and obvious normal form for equations which possess at least one conservation law. The geometric structure of the equation gives rise to a simple yet much less obvious normal form for equations which possess at least two conservation laws.