TY - JOUR
T1 - Integrability of and differential-algebraic structures for spatially 1D hydrodynamical systems of Riemann type
AU - Blackmore, Denis
AU - Prykarpatsky, Yarema A.
AU - Bogolubov, Nikolai N.
AU - Prykarpatski, Anatolij K.
N1 - Funding Information:
D.B. acknowledges the National Science Foundation (Grant CMMI-1029809 ), A.P. and Y.P. acknowledge the Scientific and Technological Research Council of Turkey (TUBITAK/NASU-110T558 Project) for partial support of their research. Both authors wish to thank a referee for constructive criticism of the original version of this paper, which led to several improvements in the exposition.
PY - 2014/2
Y1 - 2014/2
N2 - A differential-algebraic approach to studying the Lax integrability of a generalized Riemann type hydrodynamic hierarchy is revisited and a new Lax representation is constructed. The related bi-Hamiltonian integrability and compatible Poissonian structures of this hierarchy are also investigated using gradient-holonomic and geometric methods. The complete integrability of a new generalized Riemann hydrodynamic system is studied via a novel combination of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, a Lax representation and a related infinite hierarchy of conservation laws are obtained. In addition, the differential-algebraic approach is used to prove the complete Lax integrability of the generalized Ostrovsky-Vakhnenko and a new Burgers type system, and special cases are studied using symplectic and gradient-holonomic tools. Compatible pairs of polynomial Poissonian structures, matrix Lax representations and infinite hierarchies of conservation laws are derived.
AB - A differential-algebraic approach to studying the Lax integrability of a generalized Riemann type hydrodynamic hierarchy is revisited and a new Lax representation is constructed. The related bi-Hamiltonian integrability and compatible Poissonian structures of this hierarchy are also investigated using gradient-holonomic and geometric methods. The complete integrability of a new generalized Riemann hydrodynamic system is studied via a novel combination of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, a Lax representation and a related infinite hierarchy of conservation laws are obtained. In addition, the differential-algebraic approach is used to prove the complete Lax integrability of the generalized Ostrovsky-Vakhnenko and a new Burgers type system, and special cases are studied using symplectic and gradient-holonomic tools. Compatible pairs of polynomial Poissonian structures, matrix Lax representations and infinite hierarchies of conservation laws are derived.
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U2 - 10.1016/j.chaos.2013.11.012
DO - 10.1016/j.chaos.2013.11.012
M3 - Article
AN - SCOPUS:84891621379
SN - 0960-0779
VL - 59
SP - 59
EP - 81
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
ER -