Combined sinh-cosh-Gordon equation: symmetry reductions, exact solutions and conservation laws. (English) Zbl 1397.35152
Summary: In this paper we study the combined sinh-cosh-Gordon equation, which arises in mathematical physics and has a wide range of scientific applications that range from chemical reactions to water surface gravity waves. We employ Lie symmetry analysis along with the simplest equation method to obtain exact solutions based on the optimal systems of one-dimensional subalgebras for the combined sinh-cosh-Gordon equation. Furthermore, conservation laws for the combined sinh-cosh-Gordon equation are derived by employing two different methods; the direct method and new conservation theorem.
MSC:
35L71 | Second-order semilinear hyperbolic equations |
35A30 | Geometric theory, characteristics, transformations in context of PDEs |
35L65 | Hyperbolic conservation laws |
70H33 | Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics |