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Fig.1 (Color online) The exhibition of the lump solution to $(2+1)$-dimensional Ito equation. (a) shows the lump structure at $t=0$. (b) is the projective density plot of $u$ at $t=0$. (c) shows the lump solution is moving along the straight line with a constant speed at different $t=-60$, $t=0$, and $t=60$. (d) shows the wave height in $y=0$ for $t=0$ in red, $t=-5$ in green, and $t=5$ in the blue.
Fig.2 (Color online) The evolution plot of the interaction of the lump and a stripe soliton with parameters selections in Eqs. (23) and (24) at times (a) $t=-8$, (b) $t=-1$, (c) $t=0$ and (d) $t=5$ respectively.
Fig.3 (Color online) The evolution plot of the interaction of the lump and a pair of stripe solitons with parameters selections in Eq. (23) and (24) at times (a) $t=-6$, (b) $t=-2$, (c) $t=0$ and (d) $t=2$ (e) $t=8$.
Fig.1 The distribution of the energy spectra $\epsilon$ versus $\mu$ $(n=M=\omega =\rho =1)$.
Fig.2 The distribution of the energy spectra $\epsilon$ versus $\mu$ $(n=M=\omega =\rho =1)$.
Fig.3 The distribution of the energy spectra $\epsilon$ versus $\mu$ $(n=M=\omega =\rho =1)$.
Fig.4 The distribution of the energy spectra $\epsilon$ versus $\mu$ $(n=M=\omega =\rho =1)$.
Fig.5 The distribution of the energy spectra $\epsilon$ versus $\mu$ $(n=M=\omega =\rho =1)$.
Fig.6 The distribution of the energy spectra $\epsilon$ versus $\mu$ $(n=M=\omega =\rho =1)$.
Fig.7 The distribution of the energy spectra $\epsilon$ versus $d$ $({n}'=\tilde{M}=\tilde{\omega }=\rho _{m}=1)$.
Fig.8 The distribution of the energy spectra $\epsilon$ versus $d$ $({n}'=\tilde{M}=\tilde{\omega }=\rho _{m}=1)$.
Fig.9 The distribution of the energy spectra $\epsilon$ versus $d$ $({n}'=\tilde{M}=\tilde{\omega }=\rho _{m}=1)$.
Fig.10 The distribution of the energy spectra $\epsilon$ versus $d$ $({n}'=\tilde{M}=\tilde{\omega }=\rho _{m}=1)$.
Fig.11 The distribution of the energy spectra $\epsilon$ versus $d$ $({n}'=\tilde{M}=\tilde{\omega }=\rho _{m}=1)$.
Fig.12 The distribution of the energy spectra $\epsilon$ versus $d$ $({n}'=\tilde{M}=\tilde{\omega }=\rho _{m}=1)$.
Fig.1 Non-dimensional velocity outline along $\zeta$ for various values of slip parameter $\eta$ corresponding to ramped temperature of plate with $\tau=0.8$, $Pr= 0.71$, and $Sc=0.16$.
Fig.2 Non-dimensional velocity outline for different type values of slip parameter $\eta$ corresponding to stepped temperature of the plate with $\tau=1.2$, $Pr= 0.71$, and $Sc=0.16$.
Fig.3 Non-dimensional velocity outline for different values of slip parameter $\eta$ corresponding to stepped and ramped temperature of the plate with $\tau=3$, $Pr= 0.71$, and $Sc=2.01$.
Fig.4 Non-dimensional velocity outline for various value of $N$ corresponding to ramped and stepped temperature of the plate with $\tau=3$, $Pr= 0.71$, and $Sc=2.01$.
Fig.5 Non-dimensional velocity outline for various value of $\tau$ corresponding to ramped and stepped temperature of the plate with $\eta=0.9$, $Pr= 0.71$, and $Sc=2.01$.

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