Solitons and rouge waves for a generalized ()-dimensional variable-coefficient Kadomtsev-Petviashvili equation in fluid mechanics

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• 作者：Jun Chai ; Bo Tian ; ^{tian_bupt@163.com" class="auth_mail" title="E-mail the corresponding author} ; Wen-Rong Sun ; Xi-Yang Xie
• 关键词：Fluid mechanics ; Generalized (3+13+1)-dimensional variable-coefficient Kadomtsev&ndash ; Petviashvili equation ; Auto-Bä ; cklund transformation ; Solitons ; Rouge waves ; Homoclinic breather waves
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：71
• 期：10
• 页码：2060-2068
• 全文大小：1626 K

文摘

Evolution of the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in fluid mechanics in three spatial dimensions can be described by a generalized (3+1$3+1$)-dimensional variable-coefficient Kadomtsev–Petviashvili equation, which is studied in this paper with symbolic computation. Via the truncated Painlevé expansion, an auto-Bäcklund transformation is derived, based on which, under certain variable-coefficient constraints, one-soliton, two-soliton, homoclinic breather-wave and rouge-wave solutions are respectively obtained via the Hirota method. Graphic analysis shows that the soliton propagates with the varying soliton direction. Change of the value of any one of g(t)$g\left(t\right)$, m(t)$m\left(t\right)$, n(t)$n\left(t\right)$, h(t)$h\left(t\right)$, q(t)$q\left(t\right)$ and l(t)$l\left(t\right)$ in the equation can cause the change of the soliton shape, while the soliton amplitude cannot be affected by that change, where g(t)$g\left(t\right)$ represents the dispersion, m(t)$m\left(t\right)$ and n(t)$n\left(t\right)$ respectively stand for the disturbed wave velocities along the y$y$ and z$z$ directions, h(t)$h\left(t\right)$, q(t)$q\left(t\right)$ and l(t)$l\left(t\right)$ are the perturbed effects, y$y$ and z$z$ are the scaled spatial coordinates, and t$t$ is the temporal coordinate. Soliton direction and type of the interaction between the two solitons can vary with the change of the value of g(t)$g\left(t\right)$, while they cannot be affected by m(t)$m\left(t\right)$, n(t)$n\left(t\right)$, h(t)$h\left(t\right)$, q(t)$q\left(t\right)$ and l(t)$l\left(t\right)$. Homoclinic breather wave and rouge wave are respectively displayed, where the rouge wave comes from the extreme behaviour of the homoclinic breather wave.