Necessary conditions of coupled mKdV-BLMP system for multiple-soliton solutions to exist

In this paper, we use the simplified bilinear method to solve the modified KdV and the potential Boiti?Leon?Manna?Pempinelli equation which are discussed by Wazwaz (2016) when a ? 3 and c ? 3 2. We find the necessary conditions in order that this problem has solutions. We test the proposed method by two ways. The first one, by taking a ? 3 and c ? 3 2. We find that the proposed method produces exactly the same solution found by Wazwaz (2016). Secondly, we compare our results using the proposed method with the tanh method and find that the two methods produce the same solutions. From these two comparisons, we conclude that the proposed method is efficient and the solutions produced by the simplified bilinear method are correct.