A variety of completely integrable Calogero–Bogoyavlenskii–Schiff equations with time-dependent coefficients

Abstract

PurposeThe purpose of this paper is to introduce a variety of new completely integrable Calogero–Bogoyavlenskii–Schiff (CBS) equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for each of the developed models.Design/methodology/approachThe newly developed models with time-dependent coefficients have been handled by using the simplified Hirota’s method. Moreover, multiple complex soliton solutions are derived by using complex Hirota’s criteria.FindingsThe developed models exhibit complete integrability, for specific determined functions, by investigating the compatibility conditions for each model.Research limitations/implicationsThe paper presents an efficient algorithm for handling integrable equations with analytic time-dependent coefficients.Practical implicationsThe work presents new integrable equations with a variety of time-dependent coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions.Social implicationsThis study presents useful algorithms for finding and studying integrable equations with time-dependent coefficients.Originality/valueThe paper gives new integrable CBS equations which appear in propagation of waves and provide a variety of multiple real and complex soliton solutions.