Bilinear Bäcklund transformation, kink and breather-wave solutions for a generalized (2+1)-dimensional Hirota–Satsuma–Ito equation in fluid mechanics
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China
Accepted: 13 December 2020
Published online: 1 February 2021
Fluid mechanics studies are applied in the turbines, airplanes, ships, rivers, windmills, pipes, etc. Under investigation is a generalized (2+1)-dimensional Hirota–Satsuma–Ito equation in fluid mechanics. Via the Hirota bilinear method, bilinear Bäcklund transformation is obtained, based on which the kink solutions are constructed. Breather-wave solutions are constructed via the extended homoclinic test approach. When the periods of the breather-wave solutions tend to infinity, the lump solutions are derived. It is found that the amplitudes and shapes of the breather waves keep unchanged during the propagation. Effects of the coefficients in the equation on the amplitudes and velocities for the breather waves are analyzed graphically.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021