No abstract

No abstract

The prime objective of this paper is to obtain the exact soliton solutions by applying the two mathematical techniques, namely, Lie symmetry analysis and generalized exponential rational function (GERF) method to the (2+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petviashvili (g-CHKP) equation. First, we obtain Lie infinitesimals, possible vector fields, and commutative product of vectors for the g-CHKP equation. By the means of symmetry reductions, the g-CHKP equation reduced to various nonlinear ODEs. Subsequently, we implement the GERF method to the reduced ODEs with the help of computerized symbolic computation in Mathematica. Some abundant exact soliton solutions are obtained in the shapes of different dynamical structures of multiple-solitons like one-soliton, two-soliton, three-soliton, four-soliton, bell-shaped solitons, lump-type soliton, kink-type soliton, periodic solitary wave solutions, trigonometric function, hyperbolic trigonometric function, exponential function, and rational function solutions. Consequently, the dynamical structures of attained exact analytical solutions are discussed through 3D-plots via numerical simulation. A comparison with other results is also presented.

No abstract

In this paper, a formal and systematic method for balancing chemical reaction equations was presented. The results satisfy the law of conservation of matter, and confirm that there is no contradiction to the existing way(s) of balancing chemical equations. A chemical reaction which possesses atoms with fractional oxidation numbers that have unique coefficients was studied. In this paper, the chemical equations were balanced by representing the chemical equation into systems of linear equations. Particularly, the Gauss elimination method was used to solve the mathematical problem with this method, it was possible to handle any chemical reaction with given reactants and products.