Decay of parametric solitons in a lossy medium with quadratic nonlinearity

An investigation is made into the evolution of two-wave solitons in a second-harmonic-generation system under the action of weak dissipation. Using the balance equation for the soliton energy and a previously developed variational approximation for its shape, a general evolutional equation is derived for the soliton parameters. The equation is solved explicitly for the asymptotic stage of the evolution.

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