A study of dynamics of a traveling wave and a interface in nonlinear diffusion equations

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The diffusion phenomenon of the nonlinear system appears in a lot of fields like physics, chemistry, biology, and recently, the financial engineering etc. In them, the localized structure that is called an interface where a rapid state variation concentrates on the narrow confine appears, and there are a lot that understanding the behavior that this interface shows becomes a key to clarify a nonlinear phenomenon. The traveling wave solution is a special solution that composes this interface. In the present study, the dynamics of the interface and the traveling wave in the nonlinear diffusion phenomenon was mathematically analyzed.