One method of solving these equations requires finding two operators L and P such that their commutator is equal to the time derivative of L; L and P are called a Lax pair.
Hans Lewy gave a namesake "example" of one of these equations to show that the converse of the CauchyÂ–Kovalevskaya theorem doesn't hold. A method of solving these equations generalizes the use of Adomian polynomials by employing a homotopy transformation; that is the HAM method. One method of solving these equations requires finding two operators L and P such that their commutator is equal to the time derivative of L; L and P are called a Lax pair. Another method of solving them relies on first solving along a characteristic curve. Examples of these equations include one modelling vibrating membranes in three dimensions and one modelling heat flow. For 10 points, name this type of equation which contains several variables and their derivatives.
Hans Lewy gave a namesake "example" of one of these equations to show that the converse of the CauchyÂ–Kovalevskaya theorem doesn't hold.
partial differential equations [or PDEs; prompt on "differential equations"; do not accept "ordinary differential equations" or "ODEs"]