New reductions of integrable matrix PDEs: $Sp(m)$-invariant systems
Abstract
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.
Cite
@article{arxiv.0712.4373,
title = {New reductions of integrable matrix PDEs: $Sp(m)$-invariant systems},
author = {Takayuki Tsuchida},
journal= {arXiv preprint arXiv:0712.4373},
year = {2011}
}
Comments
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 $x$-derivatives of elementary functions. Explicit soliton solutions are given in the author's talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida/