@article{JMAG_2018_14_2_a3,
author = {V. Fenchenko and E. Khruslov},
title = {Nonlinear dynamics of solitons for the vector modified {Korteweg{\textendash}de} {Vries} equation},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {153--168},
year = {2018},
volume = {14},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2018_14_2_a3/}
}
TY - JOUR AU - V. Fenchenko AU - E. Khruslov TI - Nonlinear dynamics of solitons for the vector modified Korteweg–de Vries equation JO - Žurnal matematičeskoj fiziki, analiza, geometrii PY - 2018 SP - 153 EP - 168 VL - 14 IS - 2 UR - http://geodesic.mathdoc.fr/item/JMAG_2018_14_2_a3/ LA - en ID - JMAG_2018_14_2_a3 ER -
V. Fenchenko; E. Khruslov. Nonlinear dynamics of solitons for the vector modified Korteweg–de Vries equation. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 2, pp. 153-168. http://geodesic.mathdoc.fr/item/JMAG_2018_14_2_a3/
[1] M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform, SIAM Studies in Applied Mathematics, 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa., 1981 | MR | Zbl
[2] S. C. Anco, N. T. Ngatat, M. Willoughby, “Interaction properties of complex mKdV solitons”, Phys. D, 240 (2011), 1378–1394 | DOI | MR | Zbl
[3] Ju. M. Balakhnev, A. G. Meshkov, “On a classification of integrable vectorial evolutionary equations”, J. Nonlinear Math. Phys., 15 (2008), 212–226 | DOI | MR | Zbl
[4] F. Calogero, A. Degasperis, Spectral Transform and Solitons, v. I, Studies in Mathematics and its Applications, 13, Tools to Solve and Investigate Nonlinear Evolution Equations ; Lecture Notes in Computer Science, 144, North-Holland Publishing Co., Amsterdam–New York, 1982 | MR | Zbl
[5] P. Drazin, R. S. Johnson, Solitons: an Introduction, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1989 | MR | Zbl
[6] L. D. Faddeev, L. A. Takhtajan, Hamiltonian Methods in the Theory of Solitons, Translated from the Russian by A. G. Reyman, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987 | MR | Zbl
[7] C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura, “Method for solving the Korteweg–deVries equation”, Phys. Rev. Lett., 19 (1967), 1095–1097 | DOI | MR
[8] F. A. Khalilov, E. Ya. Khruslov, “Matrix generalisation of the modified Korteweg–de Vries equation”, Inverse Problems, 6 (1990), 193–204 | DOI | MR | Zbl
[9] A. M. Kosevich, B. A. Ivanov, A. S. Kovalev, Nonlinear Wave Magnetization. Dynamic and Topological Solitons, Naukova Dumka, Kiev, 1983 (Russian)
[10] G. L. Lamb, Elements of Soliton Theory, Pure and Applied Mathematics, A Wiley-Interscience Publication, John Wiley Sons, Inc., New York, 1980 | MR | Zbl
[11] D. C. Mattis, The Theory of Magnetism. II: Thermodynamics and Statistical Mechanics, Springer-Verlag, Berlin–Heidelberg–New York–Tokyo, 1985
[12] E. N. Pelinovsky, E. G. Shurgalina, “Two-soliton interaction within the framework of the modified Korteweg–de Vries equation”, Radiophys. Quantum El., 57 (2014), 737–744 | DOI | MR
[13] V. V. Sokolov, T. Wolf, “Classification of integrable polynomial vector evolution equations”, J. Phys. A, 34 (2001), 11139–11148 | DOI | MR | Zbl
[14] Theoret. and Math. Phys., 100 (1994), 959–96 | DOI | MR | Zbl
[15] T. Tsuchida, Multisoliton solutions of the vector nonlinear Schredinger equation (Kulish–Sklyanin model) and the vector mKdV equation, arXiv: 1512.01840
[16] M. Wadati, K. Ohkuma, “Multiple-pole solutions of the modified Korteweg–de Vries equation”, J. Phys. Soc. Jpn., 51 (1982), 2029–2035 | DOI | MR