The N loop soliton solution of the Vakhnenko equation

AJ Morrison, EJ Parkes, VO Vakhnenko - Nonlinearity, 1999 - iopscience.iop.org
AJ Morrison, EJ Parkes, VO Vakhnenko
Nonlinearity, 1999iopscience.iop.org
An exact N loop soliton solution to the Vakhnenko equation (VE) is found, where N 2 is an
arbitrary positive integer. The key step in finding this solution is to transform the independent
variables in the equation. This leads to a transformed equation for which it is straightforward
to find an exact explicit N-soliton solution by using Hirota's method. The exact N loop soliton
solution to the VE is then found in implicit form by means of a transformation back to the
original independent variables. The shifts that occur when the solitons interact are found …
Abstract
An exact N loop soliton solution to the Vakhnenko equation (VE) is found, where N 2 is an arbitrary positive integer. The key step in finding this solution is to transform the independent variables in the equation. This leads to a transformed equation for which it is straightforward to find an exact explicit N-soliton solution by using Hirota's method. The exact N loop soliton solution to the VE is then found in implicit form by means of a transformation back to the original independent variables. The shifts that occur when the solitons interact are found. The general results and details of the interaction between solitons are illustrated for the case N= 3.
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