in this paper we obtain  exact solutions of the generalized kuramoto-sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    the methods used  to determine the exact solutions of the underlying equation are the lie group analysis  and the simplest equation method. the solutions obtained are  then plotted.

this paper aims to study a generalized double sinh-gordon equation, which appears in several physical phenomena such as integrable quantum field theory, kink dynamics and fluid dynamics. lie symmetry analysis together with the simplest equation method is used to obtain exact solutions for this equation. moreover, we derive conservation laws for the equation by using two different approaches, na...

We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A−G based on the explicit construction of weight states. This straightforward approach (which is slower and more memoryconsumptive than the standard methods to just calculate dimensions of the tensor product decomposition) produces Clebsch-Gordan coefficients that are of intere...

Abstract: In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspace...

where ξ is a real-valued function and η is a 2 × 2 matrix complex-valued function, a Lie symmetry of system (1) if commutation relation [L,X] = R(x)L, (4) holds with some 2× 2 matrix function R(x) (for details, see, e.g., Ref. [3]). A simple computation shows that if X is a Lie symmetry of system (1), then an operator X + r(x)L with a smooth function r(x) is its Lie symmetry as well. Hence we c...