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

VL - 43

SP - 65

EP - 90

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

IS - A

ER -