# EXPLICIT-IMPLICIT SPLITTING SCHEMES FOR SOME SYSTEMS OF EVOLUTIONARY EQUATIONS

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The evolution equation ut=uxxx+3(uxxu2 +3u2xu)+3uxu4, u=u(x,t), is integrable; it can be (exactly) linearized by an appropriate change of (dependent) variable. Hence several explicit solutions of the partial differential equation (PDE) can be exhibited; some of them display a remarkable...

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In this paper, an algebraic method to obtain the solution of linear partial differential equations of the evolution type is discussed. The proposed method exploits the Lie differential operators and their matrix realization, to reduce the equation to an easily solvable generalized matrix form....