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High-order localized waves in the (2+1)-dimensional Ito equation

In this paper, we mainly investigate the high-order localized waves in the (2+1)-dimensional Ito equation. By introducing a translation parameter and employing the Hirota derivative operator, we construct and analyze three kinds of high-order localized waves with a translation parameter: high-order line soliton, lump-type localized wave and their hybrid solutions. The obtained results show that nonlinear localized waves with a translation parameter have more plentiful dynamical behaviors. It is shown that the plus and minus resonance phenomena of two line solitons can be controlled by a translation parameter. The direction of propagation and symmetry characteristics of lump-type localized wave can be also governed by this translation parameter. Through analyzing the time delay effect we finally discuss and demonstrate the absorb-emit and emit-absorb interactions between a line soliton and a lump-type localized wave.