Transdimensional dynamics of Kerr cavity solitons

We study the bifurcation and stability of radial symmetric solitons in one- (1D), two- (2D), and three-dimensional (3D) damped-driven Kerr cavity systems. We employ a dimension-parameterized one-dimensional framework, by imposing symmetry, where the dimension of the systems can be adjusted by a real parameter, enabling us to analyze the impact of the dimensionality increase, in a continuous fashion, on the system's dynamics. Our results applied to Kerr cavity solitons unveil how key bifurcations, such as Hopf or exponential instabilities, appear in the system and reveal that the soliton solutions tend to become more and more unstable in systems with increased dimensions. Consequently, the stability region for 2D solitons is much narrower than in 1D, and all 3D solitons are unstable against collapse in the 3D damped-driven nonlinear Schrödinger equation. Our results and methods may be applied to other physically relevant 1D, 2D, 3D systems under symmetric conditions.