Singular 1-soliton and Periodic Solutions to the Nonlinear Fisher-Type Equation with Time-Dependent Coefficients

In this article,we establish exact solutions for the variable-coefficient Fisher-type equation.The solutions are obtained by the modified sine-cosine method and ansatz method.The soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz method.These solutions are important for the explanation of some practical physical problems.The obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients.