Matrix equations of hydrodynamic type as lower - dimensional reductions of Self - dual type S - integrable systems

نویسنده

  • A I Zenchuk
چکیده

We show that matrix Q × Q Self-dual type S-integrable Partial Differential Equations (PDEs) possess a family of lower-dimensional reductions represented by the matrix Q × n 0 Q quasilinear first order PDEs solved in [29] by the method of characteristics. In turn, these PDEs admit two types of available particular solutions: (a) explicit solutions and (b) solutions described implicitly by a system of non-differential equations. The later solutions, in particular, exhibit the wave profile breaking. Only first type of solutions is available for (1+1)-dimensional nonlinear S-integrable PDEs. (1+1)-dimensional N-wave equation, (2+1)-and (3+1)-dimensional Pohlmeyer equations are represented as examples. We also represent a new version of the dressing method which supplies both classical solutions and solutions with wave profile breaking to the above S-integrable PDEs.

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تاریخ انتشار 2008