Painlevé analysis for new (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equations with constant and time-dependent coefficients

Abstract

PurposeThe purpose of this paper is to introduce two new (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equations, the first with constant coefficients and the other with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for the two developed models.Design/methodology/approachThe newly developed models with constant coefficients and with time-dependent coefficients have been handled by using the simplified Hirota’s method. The author also uses the complex Hirota’s criteria for deriving multiple complex soliton solutions.FindingsThe two developed BLMP models exhibit complete integrability for any constant coefficient and any analytic time-dependent coefficients by investigating the compatibility conditions for each developed model.Research limitations/implicationsThe paper presents an efficient algorithm for handling integrable equations with constant and analytic time-dependent coefficients.Practical implicationsThe paper presents two new integrable equations with a variety of coefficients. The author showed that integrable equations with constant and time-dependent coefficients give real and complex soliton solutions.Social implicationsThe paper presents useful algorithms for finding and studying integrable equations with constant and time-dependent coefficients.Originality/valueThe paper presents an original work with a variety of useful findings.