Delta-Shock Interactions and Soliton-like Solutions in a Shallow-Water Conservation Law

Delta-shock wave interactions are analysed in the one-dimensional shallow-water system with variable bottom topography. The problem is formulated in a distributional framework that accommodates Dirac delta initial data in all state variables. Explicit solutions are constructed and shown to exhibit coherent, soliton-like behaviour across all variables, identifying a subclass of delta-shock waves with dynamics closely analogous to classical solitons.