Abstract
In this paper, based on Hirota bilinear form, we aim to show the diversity of interaction solutions to the (2 + 1)-dimensional Sawada-Kotera (SK) equation. By introducing an arbitrary differentiable function in assumption form, we can obtain abundant interaction solutions which can provide the possibility for exploring the interactions between lump waves and other kinds of waves. By choosing some particular functions and values of the involved parameters, we give four illustrative examples of the resulting solutions, and explore some novel interaction behaviors in (2 + 1)-dimensional SK equation.
Highlights
As we all known, integrable nonlinear evolution equations have soliton solutions, which reflect a common nonlinear phenomenon in nature
In this paper, based on Hirota bilinear form, we aim to show the diversity of interaction solutions to the (2 + 1)-dimensional Sawada-Kotera (SK) equation
Via the Hirota bilinear form, we have studied the (2 + 1)-dimensional Sawada-Kotera equation
Summary
Integrable nonlinear evolution equations have soliton solutions, which reflect a common nonlinear phenomenon in nature. The rational rogue waves and lump waves exponentially localized solutions in certain directions. Lump wave is a kind of special wave, rationally localized in all directions in the space. The lump solution for its significant physical meanings was first discovered by Manakov et al [1]. Many integrable equations have been found to possess lump solutions, such as the KP equation [2] [3] [4], the two-dimensional nonlinear Schrödinger type equation [3], the three-dimensional three wave resonant interaction equation [5] and the Ishimori equation [6]
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