New soliton solutions of Dual mode Sawada Kotera equation using a new form of modified Kudryashov method and the finite difference method
Khalid K. Ali, M.S. Mehanna, Abdel‐Haleem Abdel‐Aty, Abdul–Majid Wazwaz
Abstract
In this article, we suggest a new form of modified Kudryashov’s method (NMK) to study the Dual-mode Sawada Kotera model. We know very well that the more the solutions depend on many constants, the easier it is to study the model better by observing the change in the constants and what their impact is on the solutions. From this point of view, we developed the modified Kudryashov method and put it in a general form that contains more than one controllable constant. We have studied the model in this way and presented figures showing the correctness of what we hoped to reach from the proposed method. In addition to the results we reached, they were not sufficient, so we presented an extensive numerical study of this model using the finite differences method. We also came up with the local truncation error for the difference scheme is h6k2(1+k2). In addition, the analytical solutions we reached were compared with the numerical solutions, and we presented many forms that show that the results we reached are a clear contribution to this field.