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N-soliton solutions and the Hirota conditions in (1+1)-dimensions
  • Wenxiu Ma
Wenxiu Ma
College of Arts and Sciences University of South Florida

Corresponding Author:mawx@math.usf.edu

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We discuss N-soliton solutions and analyze the Hirota N-soliton conditions, starting from Hirota bilinear forms. An algorithm to verify the Hirota conditions is proposed by factoring out common factors for the terms in the conditions and comparing degrees of the involved polynomials containing the common factors. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, together with all proofs of the existence of N-soliton solutions to each equation in two classes.
23 Feb 2022Published in International Journal of Nonlinear Sciences and Numerical Simulation volume 23 issue 1 on pages 123-133. 10.1515/ijnsns-2020-0214