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The N-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation)

Morrison, A.J. and Parkes, E.J. (2003) The N-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation). Chaos, Solitons and Fractals, 16 (1). pp. 13-26. ISSN 0960-0779

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Abstract

The N-soliton solution of a new nonlinear evolution equation, the modified generalised Vakhnenko equation, is found. 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 type decomposition. Different types of soliton are possible, namely loops, humps or cusps. Details of the different types of interactions between solitons are discussed in detail for the case N=2. A proof of the 'N-soliton condition' is given in Appendix A.