RETRACTED: New interaction solutions to the (2 + 1)-dimensional Hirota–Satsuma–Ito equation

Soliton solutions and their degenerations in the (2+1)-dimensional Hirota–Satsuma–Ito equations with time-dependent linear phase speed

“…Different choose of the function γ(t) will lead to the different line soliton solutions of the equations (7). Here are two examples.…”

“…One breather soliton. Let a 1 and a 2 , b 1 and b 2 be the conjugate complex numbers respectively, and η 01 = η 02 = 0, we get the periodic soliton solutions of the equations (7).…”

“…Considering N = 4, for i from 1 to 4, a i and b i are assumed as real numbers, and η 0i = 0 in formula (11), we can get the four lines soliton solutions of the equations (7), which may be U-shape or S-shape as γ(t) is a positive-integer-power function of t. There is no figure here for nothing novel.…”

“…Nonlinear integrable systems describe a great deal of physical phenomena in natural sciences and engineering applications. In the paste decades, many scholars work on finding the analytical and numerical solutions to the nonlinear partial differential equations and many distinctive solving techniques came out one after another, such as the Hirota bilinear method [1]- [7], the Bäcklund transformation [8]- [10], the Darboux transformation [11]- [13], the inverse scattering method [14]- [17], the Lie group method [18]- [20] and so on. These approaches play a major role in constructing exact solutions and work well in studying the integrable systems.…”

“…A verified HSI equation was proposed in [5], and many types soliton solutions were constructed and their interactions were discussed. Some analytical lump solutions were determined in [7] and the physical behaviors involved in the solutions were also described. The novelty of this paper lies in the fact that we consider the (2+1)-dimensional HSI equation with time-dependent coefficients of the form…”