Carpio Rodríguez, Ana MaríaChapman, S. J.Hastings, S.Mcleod, J. B.2023-06-202023-06-202000Carpio Rodríguez, A. M., Chapman, S. J., Hastings, S. & Mcleod, J. B. «Wave Solutions for a Discrete Reaction-Diffusion Equation». European Journal of Applied Mathematics, vol. 11, n.o 4, septiembre de 2000, pp. 399-412. DOI.org (Crossref), https://doi.org/10.1017/S0956792599004222.0956-792510.1017/S0956792599004222https://hdl.handle.net/20.500.14352/57218Motivated by models from fracture mechanics and from biology, we study the infinite system of differential equations u'(n) = u(n-1) - 2u(n) + u(n+1) - A sin u(n) + F, ' = d/dt, where A and F are positive parameters. For fixed A > 0 we show that there are monotone travelling waves for F in an interval F-crit < F < A, and we are able to give a rigorous upper bound for F-crit, in contrast to previous work on similar problems. We raise the problem of characterizing those nonlinearities (apparently the more common) for which F-crit > 0. We show that, for the sine nonlinearity, this is true if A > 2. (Our method yields better estimates than this, but does not include all A > 0.) We also consider the existence and multiplicity of time independent solutions when \F\ < F-crit.engjournal articlehttps://doi.org/10.1017/S0956792599004222http://journals.cambridge.org/abstract_S0956792599004222restricted access517.9Nagumo equationSystemsPropagationEcuaciones diferenciales1202.07 Ecuaciones en Diferencias