Transverse instability of concentric solitons

Concentric water waves are among most commonly observed. In the present talk we report a construction of axisymmetric solitary waves on deep and shallow water as well as discuss the properties of the respective governing equations of the nonlinear Schrodinger and Korteweg-de Vries type, which are deduced from the complete fluid dynamics formulation with the help of multiple scales methods. By superimposing azimuthal perturbations to the constructed finite-amplitude solutions we explore their transverse instability using both spectral analysis and Hamiltonian methods, identify the transition curve depending upon the value of surface tension, and contrast with the known stability results for planar solitons on a two-dimensional water surface thereby highlighting the effect of circular geometry of the solitons.