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New exact solutions for a generalised Burgers-Fisher equation
Chaos, Solitons & Fractals ( IF 7.8 ) Pub Date : 2021-09-11 , DOI: 10.1016/j.chaos.2021.111360
J. Mendoza 1, 2 , C. Muriel 3
Affiliation  

New travelling wave solutions for a generalised Burgers-Fisher (GBF) equation are obtained. They arise from the solutions of nonlinear second-order equations that can be linearised by a generalised Sundman transformation. The reconstruction problem involves a one-parameter family of first-order equations of Chini type. Firstly we obtain a unified expression of a one-parameter family of exact solutions, few of which have been reported in the recent literature by using hitherto not interrelated procedures, such as the tanh method, the modified tanh-coth method, the Exp-function method, the first integral method, or the improved (G/G)expansion method. Upon certain condition on the coefficients of the GBF equation, the procedure successes in finding all the possible travelling wave solutions, given through a single expression depending on two arbitrary parameters, and expressed in terms of the Lerch Transcendent function. Finally, the case n=1 is completely solved, classifying all the admitted travelling wave solutions into either a one-parameter family of exponential solutions, or into a two-parameter family of solutions that involve Bessel functions and modified Bessel functions. For particular subclasses of the GBF equation new families of solutions, depending on one or two arbitrary parameters and given in terms of the exponential, trigonometric, and hyperbolic functions, are also reported.



中文翻译:

广义 Burgers-Fisher 方程的新精确解

获得了广义 Burgers-Fisher (GBF) 方程的新行波解。它们产生于非线性二阶方程的解,可以通过广义 Sundman 变换线性化。重建问题涉及一个单参数族的 Chini 型一阶方程。首先,我们通过使用迄今为止不相关的程序,例如 tanh 方法、改进的 tanh-coth 方法、Exp 函数,获得了精确解的单参数族的统一表达式,其中很少在最近的文献中报道方法,第一积分法,或改进的(G/G)-扩展方法。在 GBF 方程系数的特定条件下,该过程成功地找到了所有可能的行波解,通过取决于两个任意参数的单个表达式给出,并以 Lerch 超越函数表示。最后,案件n=1完全求解,将所有允许的行波解分类为指数解的单参数族,或涉及贝塞尔函数和修正贝塞尔函数的双参数解族。对于 GBF 方程的特定子类,还报告了取决于一或两个任意参数并以指数函数、三角函数和双曲线函数形式给出的新解系列。

更新日期:2021-09-12
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