Title: Soliton fission in a fluid of non-uniform depth
Abstract: A surface water wave over a bed of non-uniform depth is considered. The fluid is incompressible, inviscid and irrotational. The Hamiltonian is determined in terms of wave-only quantities using a Dirichlet-Neumann operator. By introducing an appropriate scaling regime, and considering the bottom to vary slowly, a KdV equation with variable coefficients is derived. A one-soliton solution approaching a ramp on the seabed is then considered and numerical results demonstrate the effect the ramp shape has on the birth of new solitons as the soliton passes over it.