619,973 research outputs found
Three Dimensional Reductions of Four-Dimensional Quasilinear Systems
In this paper we show that integrable four dimensional linearly degenerate
equations of second order possess infinitely many three dimensional
hydrodynamic reductions. Furthermore, they are equipped infinitely many
conservation laws and higher commuting flows. We show that the dispersionless
limits of nonlocal KdV and nonlocal NLS equations (the so-called Breaking
Soliton equations introduced by O.I. Bogoyavlenski) are one and two component
reductions (respectively) of one of these four dimensional linearly degenerate
equations
Yang-Baxter maps and the discrete KP hierarchy
We present a systematic construction of the discrete KP hierarchy in terms of SatoâWilson-type shift operators. Reductions of the equations in this hierarchy to 1+1-dimensional integrable lattice systems are considered, and the problems that arise with regard to the symmetry algebra underlying the reduced systems as well as the ultradiscretizability of these systems are discussed. A scheme for constructing ultradiscretizable reductions that give rise to YangâBaxter maps is explained in two explicit examples
New reductions of integrable matrix PDEs: -invariant systems
We propose a new type of reduction for integrable systems of coupled matrix
PDEs; this reduction equates one matrix variable with the transposition of
another multiplied by an antisymmetric constant matrix. Via this reduction, we
obtain a new integrable system of coupled derivative mKdV equations and a new
integrable variant of the massive Thirring model, in addition to the already
known systems. We also discuss integrable semi-discretizations of the obtained
systems and present new soliton solutions to both continuous and semi-discrete
systems. As a by-product, a new integrable semi-discretization of the Manakov
model (self-focusing vector NLS equation) is obtained.Comment: 33 pages; (v4) to appear in JMP; This paper states clearly that the
elementary function solutions of (a vector/matrix generalization of) the
derivative NLS equation can be expressed as the partial -derivatives of
elementary functions. Explicit soliton solutions are given in the author's
talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida
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