Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1982 · 64 citations · 10 references
Natural SciencesMathematicsComputational Fluid DynamicsDifferential EquationsDynamical SystemsBoundary ConditionsPartial Differential EquationsBäcklund TransformationsNonlinear Partial Differential EquationsParabolic Partial Differential Equations
Abstract Bäcklund transformations (BTs) are considered for nonlinear parabolic equations of the form ut + uxx + H(ux, u, x, t) = 0. (*) The most general form of both the BT and the class (*) is adopted, and we show that the only nonlinear equations (*) possessing BTs are the slight generalizations of Burgers’ equation obtained by adding a forcing term, ut + uxx + 2uux + a(x, t) = 0.
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A symmetry approach to exactly solvable evolution equations
A. S. Fokas · Journal of Mathematical Physics · 1980 · 255 citations