Stability properties of solitary waves in a complex modified KdV system Original Research Article

Solitary wave solutions are studied for a system of coupled complex modified Korteweg-de Vries (KdV) equations with perturbations that break the Hamiltonian symmetry, and parameter regimes corresponding to linear instability and stability of the solitary waves are found. In addition, perturbation formulas are found for eigenvalues bifurcating from zero. The relative strengths of self- and cross-phase modulation determine the linear stability of the waves; in the non-Hamiltonian case, the location of bifurcating eigenvalues suggests a possible regime of bistability, where both “vector” (two-channel) and “scalar” (one-channel) solitary waves may persist. The proof requires the use of recently developed perturbation formulas based on the Evans function, as well as other spectral-theoretic tools.