Multiple Soliton, Lump and its Interaction Solutions For Nonlinear evolution equations

Abstract

Within this thesis, a comprehensive study is conducted on the behavior of kink-solitons, lumps, and their interaction solutions when subjected to periodic and kink waves of some nonlinear evolution equations. Among these NLEEs, new extended (3+1)-dimensional B-type Kadomtsev-Petviashvili equation and generalized (2+1)-dimensional Soliton equation are given. Through the utilization of the simplified Hirota’s bilinear method, kinksoliton solutions specially one-kink, two-kink and three-kink solutions are obtained. By the aid of direct method based on Hirota’s bilinear form lump and lump interaction solutions are obtained which includes lump interaction with stripe solutions, lump-periodic solution, breathers solutions and solitary wave solutions. Extreme value points of lump solutions are obtained to describe maximum and minimum points that give insights about the motion, amplitudes and velocities of these solutions. Physical attributes of obtained results are demonstrated by 3D plots, contour maps, density graphs, and 2D plots. It is also studied that physical dynamics changed by changing the values of parameters involved in test functions.