Abstract
Taking a model equation u t t - u x x - m 2 sin u =0, the behavior and the roles of solitons in unstable media are studied. The properties of solitons and their mutual collisions are discussed based on the exact solutions derived by the inverse scattering method. Furthermore, an initial boundary value problem of the model equation is studied numerically. It is concluded that creation of solitons serves to stabilize the system.
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