TY - JOUR
T1 - The N-soliton solution of a generalized Vakhnenko equation
AU - Morrison, A.J.
AU - Parkes, E.J.
PY - 2001/6
Y1 - 2001/6
N2 - 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 and 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.
AB - 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 and 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.
KW - N-soliton
KW - Vakhnenko equation
KW - Hirota's method
UR - http://www.maths.strath.ac.uk/~caas35/m&pGMJ01.pdf
UR - http://dx.doi.org/10.1017/S0017089501000076
U2 - 10.1017/S0017089501000076
DO - 10.1017/S0017089501000076
M3 - Article
SN - 0017-0895
VL - 43
SP - 65
EP - 90
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
IS - A
ER -