Investigation of some nonlinear physical models: exact and approximate solutions.

We use the m + 1 G ′ -expansion method in reaching the exact solution of the (3+1)-dimensional B-type Kadomtsev-Petviashvili-Boussinesq, Newel-Whitehead-Segel, and Zeldovich equations. New solutions in form of the kink, complex and singular solutions are reported. On the other hand, the Adomian decomposition method is employed to find approximate solutions to the the (3+1)-dimensional B-type Kadomtsev-Petviashvili-Boussinesq equation. The three-dimensional figures and their corresponding contour plots for the reported solutions are drawn. Also, a table is presented for the approximate solutions. The reported results may be useful in studying physical features of various nonlinear mathematical models. [ABSTRACT FROM AUTHOR]