Sasa-Satsuma hierarchy of integrable evolution equations | Zendy

Uwe Bandelow | Zendy; Adrian Ankiewicz | Zendy; Shalva Amiranashvili | Zendy; Nail Akhmediev | Zendy

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Sasa-Satsuma hierarchy of integrable evolution equations

Author(s) -

Uwe Bandelow,

Adrian Ankiewicz,

Shalva Amiranashvili,

Nail Akhmediev

Publication year - 2018

Publication title -

chaos an interdisciplinary journal of nonlinear science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.971

H-Index - 113

eISSN - 1089-7682

pISSN - 1054-1500

DOI - 10.1063/1.5030604

Subject(s) - hierarchy , integrable system , sasa , mathematics , term (time) , order (exchange) , nonlinear system , third order , relation (database) , recurrence relation , mathematical analysis , computer science , physics , quantum mechanics , paleontology , philosophy , theology , finance , economics , market economy , biology , database

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms. Up to sixth-order terms of the hierarchy are given in explicit form, while the provided recurrence relation allows one to explicitly write all higher-order terms. The whole hierarchy can be combined into a single general equation. Each term in this equation contains a real independent coefficient that provides the possibility of adapting the equation to practical needs. A few examples of exact solutions of this general equation with an infinite number of terms are also given explicitly.

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