Burgers' equation

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Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, traffic flow, and mathematical physics. Burgers' equation also plays an important role in studies of the stability and dynamics of one-dimensional solitons with respect to nonlinear transverse perturbations of finite wavelength, since such perturbations are described by the Shrira-Pesenson equation, which, in the one-way wave approximation, reduces to Burgers' equation when the underlying soliton is stable. Bateman-Burgers equation was first introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948. For a given field u ( x , t ) {\displaystyle u(x,t)} and diffusion coefficient (or kinematic viscosity, as in the original fluid mechanical context...

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