Double reduction of PDEs from the association of symmetries with conservation laws with applications (Q879524)

The association of conservation laws with Noether symmetries extended to Lie-Bäcklund and nonlocal symmetries has opened the possibilities to the extension of the theory on double reductions to partial differential equations that do not have a Lagrangian and therefore to not posses Noether symmetries. at the usage of the results [\textit{A. Kara, F. Mahomed}, Int. J. Theor. Phys. 39, No. 1, 23--40 (2000; Zbl 0962.35009)] the author develops the theory to effect a double reduction of PDEs with two independent variables, which is possible when the PDEs admit a symmetry associated with a conservation law. This theory is illustrated by applications to the linear heat equation, the sine-Gordon and BBM equations and a system of PDEs from one dimensional gas dynamics.