###### Control of Conservation Laws – An Application

REFERENCES [1] ARONOVICH, G. V.: Waterhammer influence on the control stability for hydraulic turbines , Avtom. i telemekhanika 9 (1948), 204–232. (In Russian) [2] ARONOVICH, G. V.—KARTVELISHVILI, N. A—LYUBIMTSEV, YA. K.: Waterhammer and Surge Tanks . Nauka Publ. House, Moscow, 1968. (In Russian) [3] BRESSAN, A.: Hyperbolic Systems of Conservation Laws. The One-dimensional Cauchy Problem . Oxford University Press, Oxford, 2000. [4] ČETAEV, N. G.: Stability and the classical laws , Coll. Sci. Works Kazan Aviation Inst. 5 (1936), 3

###### Conservation laws for a Boussinesq equation.

as those found by symmetry methods) can play an important role in the design and testing of numerical integrators; these solutions provide an important practical check on the accuracy and reliability of such integrators, [ 8 ]. It is known that conservation laws play a significant role in the solution process of an equation or a system of differential equations. Although not all of the conservation laws of partial differential equations (PDEs) may have physical interpretation they are essential in studying the integrability of the PDEs. For variational problems

###### Solutions and conservation laws of a generalized second extended (3+1)-dimensional Jimbo-Miwa equation

x y + k u y u x x + h ( u x t + u y t + u z t ) − k u x z = 0 , $$\begin{array}{} \displaystyle u_{xxxy}+ k \left( u_{y} u_{x}\right) _x + h (u_{xt} +u_{yt}+u_{zt})-k u_{xz} = 0 , \end{array} $$ (3) where h and k are constants. We obtain exact solutions of (3) using symmetry reductions along with simplest equation method. Furthermore, we derive conservation laws for (3) using the conservation theorem due to Ibragimov. Lie symmetry theory, originally developed by Marius Sophus Lie (1842-1899), a Norwegian mathematician, around the middle of the

###### On optimal system, exact solutions and conservation laws of the modified equal-width equation

method was applied to (1) and numerical solution of the MEW equation was obtained in [ 3 ]. In our study we use an entirely different approach to obtain new exact travelling wave solutions, namely cnoidal and snoidal wave solutions of MEW Equation (1) . Moreover, for the first time we derive conservation laws of the MEW equation by employing both the Noether approach as well as the multiplier approach. 2 Exact solutions of (1) constructed on optimal system In this section, we first compute Lie point symmetries of (1) and then use them to construct an optimal

###### Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation

scientific fields and in the theory of integrable systems. It describes the unidirectional propagation of long waves of small amplitude and has a lot of applications in a number of physical contexts such as hydromagnetic waves, stratified internal waves, ion-acoustic waves, plasma physics and lattice dynamics [ 2 ]. Equation (1) has multiple-soliton solutions and an infinite number of conservation laws and many other physical properties. See for example [ 3 , 4 , 5 ] and references therein. Recently focus has shifted to the study of coupled systems of Korteweg-de Vries

######
Genetic Diversity and Structure of Northern Populations of the Declining Coastal Plant *Eryngium maritimum*

REFERENCES Acosta, A., Carranza, M. L., Izzi, C. F. (2009). Are there habitats that contribute best to plant species. Biodivers. Conserv. , 18 , 1087–1098. Andersone, U., Druva-Lusite, I., Ievina, B., Karlsons, A., Necajeva, J., Samsone, I., Ievinsh, G. (2011). The use on nondestructive methods to assess a physiological status and conservation perspectives of Eryngium maritimum L. J. Coastal Conserv ., 15 , 509–522. Aviziene, D., Pakalnis, R., Sendzikaite, J. (2008). Status of red-listed species Eryngium maritimum L. on the Lithuanian

###### Tourism policy and management for conservation of biodiversity in the Lake Engure catchment area

://ec.europa.eu/environment/nature/biodiversity/comm2006/2020.htm Ars, M., Bohanec, M. (2010). Towards the ecotourism: A decision support model for the assessment of sustainability of mountain huts in the Alps. J. Environ. Manag. , 91 , 2554-2564. Bardach, E. (2009). A Practical Guide for Policy Analysis The Eightfold Path to More Effective Problem Solving. Washington: CQ Press. 170 pp. Garcia-Frapolli, E., Ayala-Orozco, B., Bonilla-Moheno, M, Espadas-Manrique, C., Ramos-Fernandez, G. (2007). Biodiversity conservation, traditional

###### Conservation Rules of Direct Sum Decomposition of Groups

## Summary

In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization.

###### Plum Cultivars in Sweden: History and Conservation for Future Use

. (2003). Conservation of Swedish fruit, berry and nut varieties. Nordiske genresursser, 2 (1), 12. Hjalmarsson, I. (ed.) (2007). Här bevaras våra svenska fruktsorter [Where Swedish fruit cultivars are preserved]. CBMs skriftserie 16. CBM Swedish Biodiversity Centre. 43 pp. (in Swedish). Hjalmarsson, I. (2014). Plommon Prunus domestica ‘Elam’ [Plum Prunus domestica ‘Elam’]. Tidning för Hushållningssällskapen i Jönköping, Västra Götaland och Värmland, Nr. 4, 33 (in Swedish). Hjalmarsson, I., Trajkovski, V., Wallace, B. (2008). Adaption of

###### Multiplier method and exact solutions for a density dependent reaction-diffusion equation

leading to the integration by quadrature of ordinary differential equations, to the determination of invariant solutions of initial and boundary value problems and to the derivation of conservation laws [ 2 ]. In some particular cases this equation has been studied by other authors. In the particular case of g ( u ) = 1 [ 9 ], symmetry reductions and exact solutions were obtained using classical and nonclassical symmetries. u t = u ( 1 − u ) + 1 x x u u x x , $$\begin{array}{} \displaystyle u_t=u(1-u)+\frac{1}{x}\left[xuu_x\right]_x, \end{array}$$ (2) by