RESUMEN
In this paper, complex-variable sine-Gaussian cross-phase (CVSGCP) beams are proposed, and the transmission dynamics properties of the CVSGCP beams in strongly nonlocal nonlinear media are investigated. CVSGCP beams can produce a variety of mode transformation characteristics during transmission. The roles of parameters in the sine and cross-phase terms of the initial light field expression in the evolution of light intensity modes, phase, and beam width are analyzed in detail, and it is proved that the effect of cross phase is to cause the beams to rotate. The control of different modes can be achieved by selecting suitable parameters, which have certain advantages in the practical application of CVSGCP beams. CVSGCP beams can be regarded as generalized high-order breathers because light intensity modes and beam width show periodic oscillation distribution during transmission. The typical evolution characteristics of the CVSGCP beams are verified by numerical simulation. Strongly nonlocal nonlinear optical media can be mathematically equivalent to a variety of optical systems, such as gradient index potential wells and resonant potential wells, so the conclusions in this paper can also be extended to these equivalent optical systems.