New analytical solutions and modulation instability analysis for the nonlinear (1+1)-dimensional Phi-four model

This paper deals with the nonlinear (1+1)-dimensional Phi-four equation in the sense of the Katugampola operator, which can be used to model a variety of real-world applications. To solve this equation, we propose a generalized double auxiliary equation method that yields several new exact solutions. We also use linear stability analysis to discuss the instability modulation analysis for stationary solutions. Other partial differential equations can have their exact solutions found using the proposed methodology.