Abstract

In this article, the extended multiple Riccati equations expansion method has been used to construct a series of double soliton- like solutions, double triangular function solutions and complexiton soliton solutions for some nonlinear partial differential equations in mathematical physics via the (2+1) dimensional breaking soliton equations, (2+1) dimensional painleve integrable Burger's equations and (2+1) dimensional Nizhnik- Novikov- Vesselov equations. With the help of symbolic computation as Maple or Mathematica, we obtain many new types of complexiton soliton solutions, for example, various combination of trigonometric periodic function and hyperbolic function solutions, various combination of trigonometric periodic function and rational function solutions, various combination of hyperbolic function and rational function solutions.

Key words: The extended multiple Riccati equations expansion method, double soliton-like solutions, double triangular function solutions, complexiton soliton solutions, the (2+1) dimensional breaking soliton equations, the (2+1) dimensional painleve integrable Burger's equations, the (2+1)-dimensional Nizhnik-Novikov- Vesselov equations.