Burger's equation: Generalizations and solutions
We have seen that there exist generalizations of Burgers' equation which admit closed form solutions. The analog of the terms added to the original Burgers equation is the inclusion of forcing terms in the Navier-Stokes equation.
A number of directions for future work are suggested. From the connection with the Schrödinger equation we know there are other soluble models. For example, the case of a plane electromagnetic wave incident on a charged particle can be handled. It would be of some interest to apply the various approximate and statistical techniques which have been used on the Navier-Stokes equation to our soluble model equations.
In this connection it may be mentioned that there a re other model equations due to Burgers(4) which, when suitably modified5 yield simple solutions. Similar remarks hold for these equations.
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