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SIGMA, 2006, Volume 2, 078, 12 pages (Mi sigma106)  

This article is cited in 7 scientific papers (total in 7 papers)

Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations

Anjan Kundu

Saha Institute of Nuclear Physics, Theory Group & Centre for Applied Mathematics & Computational Science, 1/AF Bidhan Nagar, Calcutta 700 064, India

Abstract: Addition of higher nonlinear terms to the well known integrable nonlinear Schrödinger (NLS) equations, keeping the same linear dispersion (LD) usually makes the system nonintegrable. We present a systematic method through a novel Eckhaus–Kundu hierarchy, which can generate higher nonlinearities in the NLS and derivative NLS equations preserving their integrability. Moreover, similar nonlinear integrable extensions can be made again in a hierarchical way for each of the equations in the known integrable NLS and derivative NLS hierarchies with higher order LD, without changing their LD.

Keywords: NLSE & DNLSE; higher nonlinearity; linear dispersion preservation; integrable Eckhaus–Kundu hierarchy

DOI: https://doi.org/10.3842/SIGMA.2006.078

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Full text: http://emis.mi.ras.ru/.../Paper078
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ArXiv: nlin.SI/0512016v2
MSC: 35G20; 37C85; 35G25; 37E99
Received: August 14, 2006; in final form October 17, 2006; Published online November 10, 2006
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Citation: Anjan Kundu, “Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations”, SIGMA, 2 (2006), 078, 12 pp.

Citation in format AMSBIB
\Bibitem{Kun06}
\by Anjan Kundu
\paper Integrable Hierarchy of Higher Nonlinear Schr\"odinger Type Equations
\jour SIGMA
\yr 2006
\vol 2
\papernumber 078
\totalpages 12
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    This publication is cited in the following articles:
    1. A. B. Khasanov, A. A. Reiimberganov, “O konechno plotnom reshenii vysshego nelineinogo uravneniya Shredingera s samosoglasovannym istochnikom”, Ufimsk. matem. zhurn., 1:4 (2009), 133–143  mathnet  zmath
    2. He Jing-Song, Xu Shu-Wei, Ruderman M.S., Erdelyi R., “State Transition Induced By Self-Steepening and Self Phase-Modulation”, Chin. Phys. Lett., 31:1 (2014), 010502  crossref  isi  scopus
    3. He J., Xu Sh., Cheng Y., “the Rational Solutions of the Mixed Nonlinear Schrodinger Equation”, AIP Adv., 5:1 (2015), 017105  crossref  adsnasa  isi  elib  scopus
    4. Qiu D., He J., Zhang Y., Porsezian K., “the Darboux Transformation of the Kundu-Eckhaus Equation”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 471:2180 (2015), 20150236  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Yuan F., Qiu D., Liu W., Porsezian K., He J., “On the evolution of a rogue wave along the orthogonal direction of the ( t, x )-plane”, Commun. Nonlinear Sci. Numer. Simul., 44 (2017), 245–257  crossref  mathscinet  isi  elib  scopus
    6. Ankiewicz A., Bandelow U., Akhmediev N., “Generalised Sasa-Satsuma Equation: Densities Approach to New Infinite Hierarchy of Integrable Evolution Equations”, Z. Naturfors. Sect. A-J. Phys. Sci., 73:12 (2018), 1121–1128  crossref  isi  scopus
    7. Shi X., Li J., Wu Ch., “Dynamics of Soliton Solutions of the Nonlocal Kundu-Nonlinear Schrodinger Equation”, Chaos, 29:2 (2019), 023120  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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