The compound (G′G)-expansion method and double non-traveling wave solutions of (2+1) -dimensional nonlinear partial differential equations

To seek the exact double non-traveling wave solutions of nonlinear partial differential equations, the compound (G′G)-expansion method is firstly proposed in this paper. With the aid of symbolic computation, this new method is applied to construct double non-traveling wave solutions of (2+1)-dimensional Painlevé integrable Burgers equation and (2+1)-dimensional breaking soliton equation. As a result, abundant double non-traveling wave solutions including double hyperbolic function solutions, double trigonometric function solutions, double rational solutions, and a series of complexiton solutions of these two equations are obtained via the proposed method. These exact solutions contain arbitrary functions, which may be helpful to explain some complex phenomena. When the parameters are taken as special values, the double solitary-like wave solutions can be derived from double hyperbolic function solutions. Furthermore, the time evolutions of double solitary-like wave solutions are discussed in detail.