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Author: Ankiewicz, Adrian × Author: Bandelow, Uwe × Has files: Yes × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: Sasa-Satsuma equation ×

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    Generalized integrable evolution equations with an infinite number of free parameters
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Akhmediev, Nail; Ankiewicz, Adrian; Amiranashvili, Shalva; Bandelow, Uwe
    Evolution equations such as the nonlinear Schrödinger equation (NLSE) can be extended to include an infinite number of free parameters. The extensions are not unique. We give two examples that contain the NLSE as the lowest-order PDE of each set. Such representations provide the advantage of modelling a larger variety of physical problems due to the presence of an infinite number of higher-order terms in this equation with an infinite number of arbitrary parameters. An example of a rogue wave solution for one of these cases is presented, demonstrating the power of the technique.
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    Generalized Sasa-Satsuma equation: Densities approach to new infinite hierarchy of integrable evolution equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Ankiewicz, Adrian; Bandelow, Uwe; Akhmediev, Nail
    We derive the new infinite Sasa-Satsuma hierarchy of evolution equations using an invariant densities approach. Being significantly simpler than the Lax-pair technique, this approach does not involve ponderous 3 x3 matrices. Moreover, it allows us to explicitly obtain operators of many orders involved in the time evolution of the Sasa-Satsuma hierarchy functionals. All these operators are parts of a generalized Sasa-Satsuma equation of infinitely high order. They enter this equation with independent arbitrary real coefficients that govern the evolution pattern of this multi-parameter dynamical system.