RT journal article
T1 Conservation Laws and Exact Solutions for Time-Delayed Burgers–Fisher Equations
A1 Márquez Lozano, Almudena del Pilar
A1 Rosa Silva, Rafael de la
A1 Garrido Letrán, Tamara María
A1 Gandarias Núñez, María Luz
A2 Matemáticas
K1 Time-delayed Burgers-Fisher equations
K1 Conservation laws
K1 Travelling waves
K1 Exact solutions
AB A generalization of the time-delayed Burgers–Fisher equation is studied. This partialdifferential equation appears in many physical and biological problems describing the interactionbetween reaction, diffusion, and convection. New travelling wave solutions are obtained. Thesolutions 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, whichis a first-order Chini equation. Under certain conditions on the coefficients of the equation, the Chinitype equation obtained can be solved, yielding travelling wave solutions expressed in terms of theLerch transcendent function. For a special case, the first integral becomes a Riccati equation, whosesolutions are given in terms of Bessel functions, and for a special case of the parameters, the solutionsare given in terms of exponential, trigonometric, and hyperbolic functions. Furthermore, a completeclassification 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.
PB Multidisciplinary Digital Publishing Institute (MDPI)
SN 2227-7390
YR 2023
FD 2023
LK http://hdl.handle.net/10498/32061
UL http://hdl.handle.net/10498/32061
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026