Painleve analysis for three integrable shallow water waves equations with time-dependent coefficients

摘要

Purpose - The purpose of this paper is concerned with investigating three integrable shallow water waves equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for these three models. Design/methodology/approach - The newly developed equations with time-dependent coefficients have been handled by using Hirota's direct method. The author also uses the complex Hirota's criteria for deriving multiple complex soliton solutions. Findings - The developed integrable models exhibit complete integrability for any analytic time-dependent coefficients defined though compatibility conditions. Research limitations/implications - The paper presents an efficient algorithm for handling time-dependent integrable equations with analytic time-dependent coefficients. Practical implications - This study introduces three new integrable shallow water waves equations with time-dependent coefficients. These models represent more specific data than the related equations with constant coefficients. The author shows that integrable equations with time-dependent coefficients give real and complex soliton solutions. Social implications - The paper presents useful algorithms for finding integrable equations with time-dependent coefficients. Originality/value - The paper presents an original work with a variety of useful findings.