Interaction phenomena between lump and solitary wave of a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation in liquid with gas bubbles*

Jian-Guo Liu,Wen-Hui Zhu,Yan He,Ya-Kui Wu

Figure 1. Lump solution u(I) with α1 = 1, α2 = 2, α3 = −1, α5 = −3, x = −5, η1 = η2 = y = 0, when $\gamma (t)=\delta (t)=\varrho (t)\,=\cos t,{\alpha }_{4}(t)=\sin t$ in (a), $\gamma (t)=\delta (t)=\varrho (t)=t,{\alpha }_{4}(t)=\sin t$ in (b) and $\gamma (t)=\cosh t$, $\varrho (t)=\exp \,t$ and α4(t) = δ(t) = t in (c).