Hasibun Naher^1,, Farah Aini Abdullah²

In this article, more general and many new travelling wave solutions have been constructed through new extension of the (G′/G)-expansion method which is known as new generalized (G′/G)-expansion method. The key idea of this technique is to take full advantage of a higher ordinary nonlinear differential equation that has five different general solutions. The presentation of the travelling wave solutions is quite new and additional parameters are also used in the solution form. To illustrate the novelty and efficiency of this method, the (3+1)-dimensional Kadomstev-Petviashvili equation is desired to be investigated. The obtained solutions reveal the wider applicability to handle higher-dimensional nonlinear problems which arising in mathematical physics.

New generalized (G′/G)-expansion method, nonlinear auxiliary equation, (3+1)-dimensional Kadomstev-Petviashvili equation, travelling wave solutions, ordinary differential equations, and analytical solutions