Conditions of excitation of new waves (LITW) at nonlinear interface and diagram of wave states in the system

We have found the conditions for the excitation of all of the possible waves in a nonlinear medium with a "negative" nonlinearity, in the case when a plane wave is incident from a linear medium upon a plane surface of the nonlinear mediums. We show that these conditions depend on only two independent parameters so that all possible states of the interface can be represented in a two-dimensional diagram. This diagram consists of regions of surface waves (SW), plane waves (PW), and so-called longitudinally inhomogeneous traveling waves (LITW) which were studied recently. The diagram includes two triple points: the first one corresponds to the intersection of boundaries between regions of SW, PW, and LITW states, while the other corresponds to the formation of the hysteresis (i.e., bistable) region between PW and LITW states.