Bilinear form, bilinear auto-Bäcklund transformation, breather and lump solutions for a (3+1)-dimensional generalised Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid or a lattice
Two-layer fluids are seen in fluid mechanics, thermodynamics and medical sciences. Lattices are seen in solid-state physics. In a two-layer liquid or a lattice, a (3 + 1)-dimensional generalised Yu–Toda–Sasa–Fukuyama equation is hereby studied with symbolic computation. Via the Hirota method, bilinear form and bilinear auto-Bäcklund transformation under certain coefficient constraints are obtained. Breather solutions are worked out based on the Hirota method and extended homoclinic test approach. Considering that the periods of breather solutions tend to infinity, we derive the lump solutions under a limit procedure. We observe that the amplitudes of the breather and lump remain unchanged during the propagation. Furthermore, we graphically present the breathers and lumps under the influence of different coefficients in the equation.
Volume 96, 2022
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