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

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

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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