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Wavefronts for a cooperative tridiagonal system of differential equations

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Consider the infinite system of nonlinear differential equations\(\dot u\) n =f(n−1, un, un+1),nεℤ, wherefεC 1,D 1 f > 0,D 3 f>0, andf(0, 0, 0) = 0 =f(1, 1, 1). Existence of wavefronts—i.e., solutions of the formu n (t) = U(n + ct), whereℝ,U(− ∞) = 0,U(+∞) = 1, andU is strictly increasing—is shown for functionsf which satisfy the condition: there existsa, 0<a<1, such thatf(x, x,x)<0 for 0<x<a andf(x, x, x) > 0 fora < x < 1.

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Hankerson, D., Zinner, B. Wavefronts for a cooperative tridiagonal system of differential equations. J Dyn Diff Equat 5, 359–373 (1993). https://doi.org/10.1007/BF01053165

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Key words

  • Traveling waves
  • Nagumo equation
  • cooperative systems
  • comparision principles