Conservation laws of generalized higher Burgers and linear evolution equations
نویسندگان
چکیده
By the Cole-Hopf transformation, with any linear evolution equation in 1 + 1 dimensions a generalized Burgers equation is associated. We describe local conservation laws of these equations. It turns out that any generalized Burgers equation has only one conservation law, while a linear evolution equation with constant coefficients has an infinite number of (x, t)independent conservation laws iff the equation involves only odd order terms and, therefore, is bi-Hamiltonian. It is well known that the classical Burgers equation vt = vxx+2vxv is obtained from the linear heat equation ut = uxx by the Cole-Hopf transformation v = ux/u, but it is less known that this construction can be applied to an arbitrary linear evolution equation ut = m
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