Abstract:Abstract.The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames is studied, using pole-decompositions as starting point. Polynomials encoding the numerically computed 2N flame-slope poles, and auxiliary ones, are found to closely follow a MeixnerPollaczek recurrence; accurate steady crest shapes ensue for N3. Squeezed crests ruled by a discretized Burgers equation involve the same polynomials. Such explicit approximate shape still lack for finite-N pole-decomposed periodi… Show more
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