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Volume 11, Issue 2
Localised Nonlinear Wave Interaction in the Generalised Kadomtsev-Petviashvili Equation

Yaqing Liu, Bo Ren & Deng-Shan Wang

East Asian J. Appl. Math., 11 (2021), pp. 301-325.

Published online: 2021-02

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  • Abstract

The Hirota bilinear scheme and $τ$-function formalism is used in the study of localised nonlinear wave interaction structures generated by the six-soliton solutions of the generalised Kadomtsev-Petviashvili equation. Employing different sets of parameters and the long wave limit method, we consider examples of interaction of various types of waves — viz. line solitons, breathers and lumps. The dynamics of the corresponding interaction is demonstrated graphically to visualise the type of actions. The results obtained may be helpful in understanding the wave propagation in liquids containing gas bubbles.

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@Article{EAJAM-11-301, author = {Liu , YaqingRen , Bo and Wang , Deng-Shan}, title = {Localised Nonlinear Wave Interaction in the Generalised Kadomtsev-Petviashvili Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {2}, pages = {301--325}, abstract = {

The Hirota bilinear scheme and $τ$-function formalism is used in the study of localised nonlinear wave interaction structures generated by the six-soliton solutions of the generalised Kadomtsev-Petviashvili equation. Employing different sets of parameters and the long wave limit method, we consider examples of interaction of various types of waves — viz. line solitons, breathers and lumps. The dynamics of the corresponding interaction is demonstrated graphically to visualise the type of actions. The results obtained may be helpful in understanding the wave propagation in liquids containing gas bubbles.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.290820.261020}, url = {http://global-sci.org/intro/article_detail/eajam/18636.html} }
TY - JOUR T1 - Localised Nonlinear Wave Interaction in the Generalised Kadomtsev-Petviashvili Equation AU - Liu , Yaqing AU - Ren , Bo AU - Wang , Deng-Shan JO - East Asian Journal on Applied Mathematics VL - 2 SP - 301 EP - 325 PY - 2021 DA - 2021/02 SN - 11 DO - http://doi.org/10.4208/eajam.290820.261020 UR - https://global-sci.org/intro/article_detail/eajam/18636.html KW - Generalised Kadomtsev-Petviashvili equation, $τ$-function formalism, waves interaction. AB -

The Hirota bilinear scheme and $τ$-function formalism is used in the study of localised nonlinear wave interaction structures generated by the six-soliton solutions of the generalised Kadomtsev-Petviashvili equation. Employing different sets of parameters and the long wave limit method, we consider examples of interaction of various types of waves — viz. line solitons, breathers and lumps. The dynamics of the corresponding interaction is demonstrated graphically to visualise the type of actions. The results obtained may be helpful in understanding the wave propagation in liquids containing gas bubbles.

Yaqing Liu, Bo Ren & Deng-Shan Wang. (2021). Localised Nonlinear Wave Interaction in the Generalised Kadomtsev-Petviashvili Equation. East Asian Journal on Applied Mathematics. 11 (2). 301-325. doi:10.4208/eajam.290820.261020
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