Group classification, conservation laws and Painlev?? analysis for Kleina??Gordona??Zakharov equations in (3+1)-dimension

摘要

In this paper, we study Kleina??Gordona??Zakharov equations which describe the propagation of strong turbulence of the Langmuir wave in a high-frequency plasma. Using the symbolic manipulation tool Maple, the classifications of symmetry algebra are carried out, and the construction of several local non-trivial conservation laws based on a direct method of Anco and Bluman is illustrated. Starting with determination of symmetry algebra, the one- and two-dimensional optimal systems are constructed, and optimality is also established using various invariant functions of full adjoint action. Apart from classification and construction of several conservation laws, the Painlev?? analysis is also performed in a symbolic manner which describes the non-integrability of equations.