Breathing wave solutions and Y-type soliton soluions of the new (3+1)-dimensional pKP-BKP equation

In this paper, we investigate the exact solutions of the (3+1)-dimensional pKP-BKP equation for describing certain nonlinear fluctuation phenomena in nonlinear optics, plasma physics and hydrodynamics. By imposing novel constraints on the N-soliton solution of this equation, we derive Y-type soliton solutions. Subsequently, through the application of complex conjugation techniques, these N-soliton solutions are converted into P-order breathing wave solutions. Furthermore, the interaction solutions are obtained by combining the Y-type soliton solutions with the breathing wave solutions during the partial degeneracy process of the N-soliton solutions. Finally, we select specific parameters to demonstrate the dynamic behaviors of the obtained solutions.