Integrability and asymptotic behaviour of a differential-difference matrix equation

PHYSICA D-NONLINEAR PHENOMENA

卷:415

Article

Gordoa, Pilar R.¹  Pickering, Andrew¹  Wattis, Jonathan A. D.² 

[1] Univ Rey Juan Carlos, ESCET, Area Matemat Aplicada, C Tulipan S-N, Madrid 28933, Spain

[2] Univ Nottingham, Sch Math Sci, Univ Pk, Nottingham NG7 2RD, England

关键词: Integrability;    Asymptotics;    Matrix equations;    Differential-difference equations;   

DOI  :  10.1016/j.physd.2020.132754

来源: Elsevier

【 摘 要 】

In this paper we consider the matrix lattice equation U-n,U-t(Un+1 - Un-1) = g(n)I, in both its autonomous (g(n) = 2) and nonautonomous (g(n) = 2n - 1) forms. We show that each of these two matrix lattice equations are integrable. In addition, we explore the construction of Miura maps which relate these two lattice equations, via intermediate equations, to matrix analogs of autonomous and nonautonomous Volterra equations, but in two matrix dependent variables. For these last systems, we consider cases where the dependent variables belong to certain special classes of matrices, and obtain integrable coupled systems of autonomous and nonautonomous lattice equations and corresponding Miura maps. Moreover, in the nonautonomous case we present a new integrable nonautonomous matrix Volterra equation, along with its Lax pair. Asymptotic reductions to the matrix potential Korteweg-de Vries and matrix Korteweg-de Vries equations are also given. (c) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free