We develop an analytical approach for describing a birth of internal modes of solitary waves in nonintegrable nonlinear models. We show that a small perturbation of a proper sign to an integrable model can create a soliton internal mode bifurcating from the continuous wave spectrum. The theory is applied to the double sine-Gordon and discrete nonlinear Schrödinger equations, and an excellent agreement with numerical data is demonstrated.

• Received 26 November 1997

DOI:https://doi.org/10.1103/PhysRevLett.80.5032