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For γ = 0 this equation reduces to the famous Fisher–Kolmogorov equation. For γ > 0 this fourth order diffusion equation has often been referred to as the Extended Fisher–Kolmogorov equation [DS] and has served as a model equation for the study of bi-stable systems arising in a variety of situations in physics [CER, CH, DS, HLS], such as second order phase transitions (Lifschitz points [Z]). The term “bi-stable” refers here to the fact that the uniform states u = ±1 are stable as solutions of the related equation

A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation