Y. Tan, J. Yang, and D.E. Pelinovsky

Semi-stability of embedded solitons in the general fifth-order KdV equation

Wave Motion 36, 241-255 (2002)

Abstract:
Evolution of perturbed embedded solitons in the general Hamiltonian fifth-order Korteweg - de Vries (KdV) equation is studied. When an embedded soliton is perturbed, it sheds a one-directional continuous-wave radiation. It is shown that the radiation amplitude is not minimal in general. A dynamical equation for velocity of the perturbed embedded soliton is derived. This equation shows that a neutrally stable embedded soliton is in fact semi-stable. When the perturbation increases the momentum of the embedded soliton, the perturbed state approaches asymptotically the embedded soliton, while when the perturbation reduces the momentum of the embedded soliton, the perturbed state decays into radiation. Our analytical results are confirmed by direct numerical simulations of the fifth-order KdV equation

Keywords:
EMBEDDED SOLITONS, FIFTH-ORDER KORTEWEG - DE VRIES EQUATION, NONLINEAR RESONANCE, AMPLITUDE EQUATIONS, RADIATION POLES