Abstract
This paper studies the PHI-four equation that arises in Quantum Mechanics. The topological 1-soliton solution or kink solution is obtained by the ansatz method. The bifurcation analysis is then subsequently carried out and several other solutions are retrieved from the analysis. These solutions include the solitary wave solutions, periodic waves and periodic singular waves. The constraint conditions also fall out from the analysis that must exist in order for the soliton solutions to exist. Thus various previous list of solutions for this equation are expanded.