New reductions of integrable matrix PDEs: $Sp(m)$-invariant systems

Details New reductions of integrable matrix PDEs: $Sp(m)$-invariant systems New reductions of integrable matrix PDEs: $Sp(m)$-invariant systems

2007-12-28

arxiv.org/abs/0712.4373v5

J. Math. Phys. 51 (2010) 053511

Nonlinear Sciences

Exactly Solvable and Integrable Systems

33 pages; (v4) to appear in JMP; This paper states clearly that the elementary function solutions of (a vector/matrix generali

Scientific paper

10.1063/1.3315862

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.

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