Application of the Tsarev generalised hodograph method to construction of solutions of three-dimensional quasilinear integrable systems of first order
摘要：We consider the hodograph method, the extended hodograph method, the generalized hodograph method. In all these cases, the problem of integrability of two-dimensional quasilinear systems of first order is reduced to the problem of integrability of linear system of first order (in partial derivatives) with variable coefficients. In a general case such systems cannot be integrated, i.e. they cannot be decomposed to infinitely many ordinary differential equations, and moreover their general solutions parameterized by arbitrary functions cannot be found. However, in the particular and important cases: where two-dimensional quasilinear systems of first order are two-dimensional reductions of three-dimensional quasilinear systems of first order, one can compute infinitely many particular solutions in implicit form.
报告人： Maxim Pavlov，Novosibirsk State University, Russia
时 间： 2018.11.28下午4：00
地 点： 逸夫楼1537