Some New Non-Travelling Wave Solutions of the Fisher Equation with Nonlinear Auxiliary Equation ANIKA TASHIN KHAN and HASIBUN NAHER* Department of Mathematics and Natural Sciences, BRAC University, 66 Mohakhali, Dhaka 1212, Bangladesh. Abstract We have generated many new non-travelling wave solutions by executing the new extended generalized and improved (G'/G)-Expansion Method. Here the nonlinear ordinary differential equation with many new and real parameters has been used as an auxiliary equation. We have investigated the Fisher equation to show the advantages and effectiveness of this method. The obtained non-travelling solutions are expressed through the hyperbolic functions, trigonometric functions and rational functional forms. Results showing that the method is concise, direct and highly effective to study nonlinear evolution equations those are in mathematical physics and engineering. Article History Received: 10-April-2018 Accepted: 29-December-2018 Keywords: New Extended Generalized and Improved (G'/G)-Expansion Method; Nonlinear Evolution Equation (NLEE); Fisher Equation; Non-Travelling Wavesolutions; Nonlinear Partial differential Equation (NLPDE). CONTACT Hasibun Naher hasibun06tasauf@gmail.com Department of Mathematics and Natural Sciences, BRAC University, 66 Mohakhali, Dhaka 1212, Bangladesh. © 2018 The Author(s). Published by Exclusive Research Publishers This is an Open Access article licensed under a Creative Commons license: Attribution 4.0 International (CC-BY). Oriental Journal of Physical Sciences www.orientjphysicalsciences.org ISSN: 2456-799X, Vol.03, No.(2) 2018, Pg. 92-101 Introduction NLEE is one of the most powerful and important model equations among all equations in nonlinear sciences and it plays a dynamic role in the field of scientific work or engineering sciences. Those reveal a lot of physical evidence which help to understand better in real world problems. That is why the explicit solutions of NLEEs play significant role in the study of physical phenomena and remains a crucial field for researchers in the ongoing investigation. For the past few decades and so on, a vast research has been carried out to find explicit solutions of NLEEs, and for that substantial work are being made by mathematicians and scientists and have developed effective and convincing methods such as the Hirota’s bilinear transformation method, 1 the tanh-coth method, 2,3 the Exp-function method, 4,5 the F-expansion method, 6 the Jacobi elliptic function method, 7 the Weierstrass elliptic function method, the homogeneous balance method, 8 the