2021
DOI: 10.1088/1402-4896/ac3154
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A new type of Darboux transformations for the one-dimensional Burgers equation with forcing

Abstract: We construct new types of arbitrary-order Darboux transformations for the stationary forced Burgers equation in one dimension. The distinguishing property of these transformations is that they generate a forcing term in the transformed Burgers equation that is inherently a one-parameter family of functions with linear dependence on the parameter. Our construction is based on an adaptation of results for Schrödinger-type equations [1].

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“…Te coal mine earthquake occurred when the stress or energy in the hypocenter area reaches critical stress or energy of coal mine earthquake [45][46][47][48]. Te strain growth in the hypocenter area during gestation of coal mine earthquakes includes the elastic strain and inelastic strain [49]. Te time history curves of stress, strain, energy, and strain rate during gestation of coal mine earthquake in Figure 10.…”
Section: Analysis Of the Coal Mine Earthquake Gestation Process Based...mentioning
confidence: 99%
“…Te coal mine earthquake occurred when the stress or energy in the hypocenter area reaches critical stress or energy of coal mine earthquake [45][46][47][48]. Te strain growth in the hypocenter area during gestation of coal mine earthquakes includes the elastic strain and inelastic strain [49]. Te time history curves of stress, strain, energy, and strain rate during gestation of coal mine earthquake in Figure 10.…”
Section: Analysis Of the Coal Mine Earthquake Gestation Process Based...mentioning
confidence: 99%