zbMATH — the first resource for mathematics

The Konno-Asai-Kakuhata system revisited: Reciprocal transformation and connection to the Kaup-Newell system. (English. Russian original) Zbl 1149.37325
J. Math. Sci., New York 151, No. 4, 3182-3184 (2008); translation from Fundam. Prikl. Mat. 12, No. 7, 163-166 (2006).
Summary: We present a chain of changes of variables that transforms a new integrable system found by K. Konno, R. Asai and H. Kakuhata [J. Phys. Soc. Japan 74, No. 7, 1881–1882 (2005; Zbl 1088.37039)] into a system of three PDEs that consists of the well-known Kaup-Newell system and a scalar first-order linear PDE on the background of the latter.
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q58 Other completely integrable PDE (MSC2000)
Full Text: DOI
[1] D. J. Kaup and A. C. Newell, ”An exact solution for a derivative nonlinear Schrödinger equation,” J. Math. Phys., 19, No. 4, 798–801 (1978). · Zbl 0383.35015
[2] K. Konno, R. Asai, and H. Kakuhata, ”A new integrable equation and its hierarchy,” J. Phys. Soc. Jpn., 74, No. 7, 1881–1882 (2005). · Zbl 1088.37039
[3] B. A. Kupershmidt, ”Dark equations,” J. Nonlinear Math. Phys., 8, No. 3, 363–445 (2001). · Zbl 1001.35107
[4] B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Their Applicatons to Gas Dynamics, Transl. Math. Monogr., 55, Amer. Math. Soc., Providence, Rhode Island (1983).
[5] S. Yu. Sakovich, ”On zero-curvature representations of evolution equations,” J. Phys. A: Math. Gen., 28, No. 10, 2861–2869 (1995). · Zbl 0834.35116
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.