Conservation Laws and Exact Solutions for Time-Delayed Burgers–Fisher Equations
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2023Department
MatemáticasSource
Mathematics - 2023, Vol. 11, n.17, pp. 1-13Abstract
A generalization of the time-delayed Burgers–Fisher equation is studied. This partial
differential equation appears in many physical and biological problems describing the interaction
between reaction, diffusion, and convection. New travelling wave solutions are obtained. The
solutions are derived in a systematic way by applying the multi-reduction method to the symmetry-
invariant conservation laws. The translation-invariant conservation law yields a first integral, which
is a first-order Chini equation. Under certain conditions on the coefficients of the equation, the Chini
type equation obtained can be solved, yielding travelling wave solutions expressed in terms of the
Lerch transcendent function. For a special case, the first integral becomes a Riccati equation, whose
solutions are given in terms of Bessel functions, and for a special case of the parameters, the solutions
are given in terms of exponential, trigonometric, and hyperbolic functions. Furthermore, a complete
classification of the zeroth-order local conservation laws is obtained. To the best of our knowledge,
our results include new solutions that have not been previously reported in the literature.
Subjects
Time-delayed Burgers-Fisher equations; Conservation laws; Travelling waves; Exact solutionsCollections
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