Re-observation on localized waves constructed by variable separation solutions of (1+1)-dimensional coupled integrable dispersionless equations via the projective Riccati equation method

Abstract

Variable separation exponential-form solution of (1+1)-dimensional coupled integrable dispersionless equations in physics and mathematics is obtained via the projective Riccati equation method. Based on the potential function, the multi-valued loop soliton, chaotic soliton chain and fractal pattern are studied. However, the singularity structure without the physical meaning is found at the same time for the original components of the system. Actually, if suitable functions are taken in variable separation solution, the singularity for the original components can be avoided. If the singularity structure for anyone of all components appears, novel and interesting structures for the potential function will become meaningless.