Shifted nonlocal reductions of 5-component Maccari system

Abstract

In this work, we prove that shifted nonlocal reductions of integrable $(2+1)$-dimensional $5$-component Maccari system are particular cases of shifted scale transformations. We present all shifted nonlocal reductions of this system and obtain new two-place and four-place integrable systems and equations. In addition to that we use the Hirota direct method and obtain one-soliton solution of the $5$-component Maccari system. By using the reduction formulas with the solution of the Maccari system we also derive soliton solutions of the shifted nonlocal reduced Maccari systems and equations. We give some particular examples of solutions with their graphs.

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