Algebraic resolution of the Burgers equation with a forcing term

A new type of Darboux transformations for the one-dimensional Burgers equation with forcing

“…Depending on the type of Darboux transformation, the functions V n , U n must be replaced by their counterparts Vn , Ûn , or  V n 2 ,  U n 2 . This means that these functions are taken from (7), (8), or (13), (14), or ( 16), (17), respectively. We see that our Darboux transformations render the transformed forcing term in the form of a sum, where the derivative of V n is multiplied by the parameter λ.…”

“…Due to its nonlinearity, the forced Burgers equation admits closed-form solutions only in very few cases. These cases include a linear forcing term in the stationary scenario [14], in the time-dependent scenario [15,16], systems that exhibit Lie symmetries [17], and models with nonhomogeneous Dirichlet boundary conditions [18]. Besides being interesting in themselves, such exactly-solvable models can be used as a basis of approximation or as a benchmark for numerical solvers.…”

Symmetry Analysis and Conservation Laws of the Boundary Value Problems for Time-Fractional Generalized Burgers' Differential Equation

“…Later Abd-el-Malek and Amin in [16] studied the symmetry analysis of the generalized (1+1)-dimensional Burgers differential equation in the formwith boundary and initial conditions u(0, x) −→ ∞, for x > 0, u(t, 0) = γr(t), for t > 0, γ = 0, and lim x→∞ u(t, x) −→ ∞, for t > 0. Some recent studies of Burgers differential equation the reader can see in [17,18]. In this research, we show the applying of Lie group analysis to study (2+1)-dimensional time-fractional generalized Burgers' differential equation with boundary and initially conditions:…”

“…Also, we find conservation laws for the nonlinear generalized Burgers' differential equation.They obtained the symmetries, according them conservation laws and some analytical solutions for above equation. Later Abd-el-Malek and Amin in [16] studied the symmetry analysis of the generalized (1+1)-dimensional Burgers differential equation in the formwith boundary and initial conditions u(0, x) −→ ∞, for x > 0, u(t, 0) = γr(t), for t > 0, γ = 0, and lim x→∞ u(t, x) −→ ∞, for t > 0.Some recent studies of Burgers differential equation the reader can see in [17,18]. In this research, we show the applying of Lie group analysis to study (2+1)-dimensional time-fractional generalized Burgers' differential equation with boundary and initially conditions:Email addresses and ORCID numbers: gulistan.iskandarova@istanbulticaret.edu.tr, https://orcid.org/0000-0001-7322-1339 (G. Iskenderoglu), dogank@ticaret.edu.tr, https://orcid.org/0000-0002-3420-7718 (D. Kaya)…”