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TMF, 2001, Volume 126, Number 1, Pages 102–114 (Mi tmf417)  

This article is cited in 16 scientific papers (total in 16 papers)

Multisoliton Solutions of the Matrix KdV Equation

V. M. Goncharenko

Finance Academy under the Government of the Russian Federation

Abstract: We consider multisoliton solutions of the matrix KdV equation. We obtain the formulas for changing phases and amplitudes during the interaction of two solitons and prove that no multiparticle effects appear during the multisoliton interaction. We find the conditions ensuring the symmetry of the corresponding solutions of the matrix KdV equation if they are constructed by the matrix Darboux transformation applied to the Schrödinger operator with zero potential.

DOI: https://doi.org/10.4213/tmf417

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English version:
Theoretical and Mathematical Physics, 2001, 126:1, 81–91

Bibliographic databases:

Received: 05.07.2000

Citation: V. M. Goncharenko, “Multisoliton Solutions of the Matrix KdV Equation”, TMF, 126:1 (2001), 102–114; Theoret. and Math. Phys., 126:1 (2001), 81–91

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Suris, YB, “Lax matrices for Yang–Baxter maps”, Journal of Nonlinear Mathematical Physics, 10 (2003), 223  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Veselov, AP, “Yang–Baxter maps and integrable dynamics”, Physics Letters A, 314:3 (2003), 214  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Ieda, J, “Matter-wave solitons in an F=1 spinor Bose–Einstein condensate”, Journal of the Physical Society of Japan, 73:11 (2004), 2996  crossref  zmath  adsnasa  isi  scopus  scopus
    4. Tsuchida, T, “N-soliton collision in the Manakov model”, Progress of Theoretical Physics, 111:2 (2004), 151  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Goncharenko V.M., Veselov A.P., “Yang–Baxter maps and matrix solitons”, New Trends in Integrability and Partial Solvability, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 132, 2004, 191–197  crossref  mathscinet  zmath  isi
    6. Zhou, RG, “An integrable decomposition of the symmetric matrix KdV equation”, Modern Physics Letters B, 22:13 (2008), 1307  crossref  zmath  adsnasa  isi  elib  scopus  scopus
    7. Boyallian, C, “Matrix-valued bispectral operators and quasideterminants”, Journal of Physics A-Mathematical and Theoretical, 41:36 (2008), 365209  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Li, CX, “Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation”, Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 464:2092 (2008), 951  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. C. R. Gilson, J. C. Nimmo, C. M. Sooman, “Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation”, Theoret. and Math. Phys., 159:3 (2009), 796–805  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Schiebold C., “The noncommutative AKNS system: projection to matrix systems, countable superposition and soliton-like solutions”, J. Phys. A: Math. Theor., 43:43 (2010), 434030  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    11. Carillo S., Schiebold C., “Matrix Korteweg-de Vries and modified Korteweg-de Vries hierarchies: Noncommutative soliton solutions”, J Math Phys, 52:5 (2011), 053507  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    12. Bondarenko N., Freiling G., Urazboev G., “Integration of the Matrix KdV Equation with Self-Consistent Source”, Chaos Solitons Fractals, 49 (2013), 21–27  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    13. Caudrelier V. Crampe N. Zhang Q.C., “Set-Theoretical Reflection Equation: Classification of Reflection Maps”, J. Phys. A-Math. Theor., 46:9 (2013), 095203  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    14. Ding Qing, He ZhiZhou, “The Noncommutative KdV Equation and Its Para-Kahler Structure”, Sci. China-Math., 57:7 (2014), 1505–1516  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Bondarenko N., “Inverse scattering on the line for the matrix Sturm–Liouville equation”, J. Differ. Equ., 262:3, 2 (2017), 2073–2105  crossref  mathscinet  zmath  isi  scopus
    16. Dimakis A. Mueller-Hoissen F., “Matrix Kp: Tropical Limit and Yang-Baxter Maps”, Lett. Math. Phys., 109:4 (2019), 799–827  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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