Nonlocal Hydrodynamic Type of Equations

Abstract

We show that the integrable equations of hydrodynamic type admit nonlocal reductions. We first construct such reductions for a general Lax equation and then give several examples. The reduced nonlocal equations are of hydrodynamic type and integrable. They admit Lax representations and hence possess infinitely many conserved quantities.

arXiv comment19 Pages

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Cited by in corpus (5)

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• Discrete Symmetries and Nonlocal Reductions
• Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces
• Local and nonlocal $(2+1)$-dimensional Maccari systems and their soliton solutions
• Soliton solutions of the shifted nonlocal NLS and MKdV equations