Chaotic Dynamics and Intense Wave Formation from Multiple Soliton Collisions and the Role of Extra Dimensions

A basic hereto unsolved puzzle of nonlinear wave dynamics is the emergence of rogue waves that, in some systems, form from a mixture of wave interaction, noise, and extreme nonlinear response, conditions in which dynamics are dominated by particle-like solitons. Previous studies have found that two-soliton interaction can result in nonreciprocal soliton amplification, a mechanism that can allow the accumulation of energy required to form rogue waves when the number of interacting solitons increases [1]. This raises a new basic question: can multiple soliton collisions (three or more) lead to amplification, or will chaotic behavior set-in, as for the well-known three-body problem for interacting particles? We experimentally and numerically explore multiple soliton collisions in conditions of strong nonreciprocal energy exchange. Experiments are carried out in a compositionally disordered photorefractive potassium-lithium-tantalate-niobate (KTN:Li) bulk crystal [2]. Here solitons are supported by a spatially local saturated Kerr-like self-focusing and energy transfer is driven by the leading nonlocal correction, the spatial analog of the nonlinear Raman effect. Comparing chaotic dynamics and intense wave formation phenomena after multiple soliton collisions, we see that if the dimensionality hosting the collision is larger than that of the nonreciprocal interaction, conditions can be found in which multiple solitons fuse without chaotic behavior. In detail, chaotic optical wave dynamics, characterized by erratic energy transfer and soliton annihilation and creation, are observed in the aftermath of a collinear three-soliton collision (Fig. 1a) [2]. When we extend the dimension of the collision, adding an extra dimension with no broken inversion symmetry, instead of chaotic behavior, the three solitons consistently fuse into an intense wave (Fig. 1 b,c) [3]. Results extend the analogy between solitons and particles to the emergence of chaos in three-body physics and provide new insight into the origin of the irregular dynamics that accompany extreme and rogue waves. In the collinear fusion analyzed in Figs. 1b, a cascade along propagation, the extra dimension is the propagation axis itself. In the noncollinear case analyzed in Fig. 1c, this extra dimension is the second transverse direction in the 2 + 1 D propagation normal to the external field. The study sheds light on how dimensionality and nonreciprocal energy exchange affect the emergence of regular and chaotic soliton behavior, suggesting that three-body physics and extra dimensionality is at the heart of soliton rogue wave formation.