Double Humped Grey and Black Solitons in Kerr Nonlinear Media

The existence of a new class of double humped grey and dark solitons in a Kerr nonlinear medium has been predicted in this paper. Following well known variational procedure, the dynamics of the propagating soliton has been converted to a Hamiltonian formulation. A set of ordinary differential equations is then derived, which was subsequently examined to predict the existence of double humped grey and dark solitons. Linear stability analysis, numerical appreciation and phase plane dynamics show that these solitons are stable.