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Conservation laws for equations related to soil water equations. (English) Zbl 1079.35004

All nontrivial conservation laws are obtained for \((2+1)\) nonlinear evolution PDE \[ u_t=(k(u)u_x)_x+(k(u)u_z)_z+l(u)u_z+p(u). \] All classes of these equations admitting point symmetries and nontrivial conservation laws are listed. It is proved that point symmetries are associated with conservation laws for special classes of these equations. Finally, acting by symmetries on the obtained conservation laws, authors produce new conservation laws.

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
76S05 Flows in porous media; filtration; seepage
58J70 Invariance and symmetry properties for PDEs on manifolds
35G25 Initial value problems for nonlinear higher-order PDEs

Keywords:

point symmetry
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