A modification of the method of characteristics: a new class of multidimensional partially integrable nonlinear systems

Details A modification of the method of characteristics: a new class of multidimensional partially integrable nonlinear systems A modification of the method of characteristics: a new class of multidimensional partially integrable nonlinear systems

2010-12-24

arxiv.org/abs/1012.5344v3

Phys.Lett.A, V.375 (2011) 2704-2713

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages

Scientific paper

We represent an algorithm reducing a big class of systems of ($M+1$)-dimensional nonlinear partial differential equations (PDEs) to the systems of $M$-dimensional first order PDEs. Thus, we integrate the original system with respect to only one independent variable reducing its dimensionality by one. For this reason we call such systems partially integrable ones. In particular, if M=1, then $M$-dimensional PDEs become ODEs. Our method may be referred to as a generalization of the method of characteristics. Possible application in hydrodynamics is discussed.

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