GAP-SOLITON HUNT IN A COUPLED KORTEWEG-DE VRIES SYSTEM

We report results of systematic numerical simulations of a system of t wo linearly coupled Korteweg-de Vries equations with opposite signs of the dispersion coefficients, in which existence of a new type of gap soliton with decaying oscillatory rails has been recently predicted by means of asymptotic analysis. We demonstrate that stable solitary wav es of this type indeed exist in this system in a form close to that pr edicted analytically while the usual Korteweg-de Vries solitary waves quickly decay into radiation. Obtaining the new solitary waves require s preparation of an initial state well-fitted to the analytically pred icted wave form. We also demonstrate that the solitary waves do not em erge in a relatively narrow vicinity of a special parametric point, wh ere the asymptotic analysis predicts a singularity.