Publication

Abstract : In this paper, we analyze the stability and dynamics of hump-like structures in single soliton solutions and the transition to ring-like structures in two soliton solutions, including their interactions. We start with the mathematical model with the effect of external potential and nonisospectral functions in the family of nonlinear Schrödinger (NLS) equation. By using the Darboux transformation method we obtain soliton solutions. Our study reveals, for the first time, that the incorporation of nonisospectral parameters induces modifications in soliton behavior, giving rise to novel interaction patterns and structural transformations. In particular, we observe that double-hump solitons exhibit instability and undergo a transition into ring soliton structures under the influence of these spectral variations. These findings provide new insights into the role of spectral modulation in shaping the evolution and stability of solitonic waves. Furthermore, we explore how variations in nonisospectral functions can lead to soliton interactions, perspectives on the dynamics.