The N-soliton solution of a generalised Vakhnenko equation
Glasgow mathematical journal, Tome 43 (2001) no. A, pp. 65-90
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The N-soliton solution of a generalised Vakhnenko equation is found, where N is an arbitrary positive integer. The solution, which is obtained by using a blend of transformations of the independent variables and Hirota's method, is expressed in terms of a Moloney & Hodnett (1989) type decomposition. Different types of soliton are possible, namely loops, humps or cusps. Details of the different types of interactions between solitons, including resonant soliton interactions, are discussed in detail for the case N=2. A proof of the ‘N-soliton condition’ is given in the Appendix.
Morrison, A. J.; Parkes, E. J. The N-soliton solution of a generalised Vakhnenko equation. Glasgow mathematical journal, Tome 43 (2001) no. A, pp. 65-90. doi: 10.1017/S0017089501000076
@article{10_1017_S0017089501000076,
author = {Morrison, A. J. and Parkes, E. J.},
title = {The {N-soliton} solution of a generalised {Vakhnenko} equation},
journal = {Glasgow mathematical journal},
pages = {65--90},
year = {2001},
volume = {43},
number = {A},
doi = {10.1017/S0017089501000076},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089501000076/}
}
TY - JOUR AU - Morrison, A. J. AU - Parkes, E. J. TI - The N-soliton solution of a generalised Vakhnenko equation JO - Glasgow mathematical journal PY - 2001 SP - 65 EP - 90 VL - 43 IS - A UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089501000076/ DO - 10.1017/S0017089501000076 ID - 10_1017_S0017089501000076 ER -
%0 Journal Article %A Morrison, A. J. %A Parkes, E. J. %T The N-soliton solution of a generalised Vakhnenko equation %J Glasgow mathematical journal %D 2001 %P 65-90 %V 43 %N A %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089501000076/ %R 10.1017/S0017089501000076 %F 10_1017_S0017089501000076
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