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Volume 3, Issue 2
Bifurcations and New Traveling Wave Solutions for the Nonlinear Dispersion Drinfel'd-Sokolov ($D(m,n)$) System

Ronghua Cheng, Zhaofu Luo & Xiaochun Hong

DOI: 10.12150/jnma.2021.193

J. Nonl. Mod. Anal., 3 (2021), pp. 193-207.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we employ the theory of the planar dynamical system to investigate the dynamical behavior and bifurcations of solutions of the traveling systems of the $D(m,n)$ equation. On the basis of the previous work of the reference [17], we obtain the solitary cusp waves solutions (peakons and valleyons), breaking wave solutions (compactons) and other periodic cusp wave solutions. Morever, we make a summary of exact traveling wave solutions to the $D(m,n)$ system including all the solutions which have been found from the references [4, 14, 17].

  • Keywords

$D(m, n)$ system, Solitary wave solution, Periodic wave solution, Compacton, Peakon.

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COPYRIGHT: © Global Science Press

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@Article{JNMA-3-193, author = {Cheng , RonghuaLuo , Zhaofu and Hong , Xiaochun}, title = {Bifurcations and New Traveling Wave Solutions for the Nonlinear Dispersion Drinfel'd-Sokolov ($D(m,n)$) System}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {3}, number = {2}, pages = {193--207}, abstract = {

In this paper, we employ the theory of the planar dynamical system to investigate the dynamical behavior and bifurcations of solutions of the traveling systems of the $D(m,n)$ equation. On the basis of the previous work of the reference [17], we obtain the solitary cusp waves solutions (peakons and valleyons), breaking wave solutions (compactons) and other periodic cusp wave solutions. Morever, we make a summary of exact traveling wave solutions to the $D(m,n)$ system including all the solutions which have been found from the references [4, 14, 17].

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2021.193}, url = {http://global-sci.org/intro/article_detail/jnma/18786.html} }
TY - JOUR T1 - Bifurcations and New Traveling Wave Solutions for the Nonlinear Dispersion Drinfel'd-Sokolov ($D(m,n)$) System AU - Cheng , Ronghua AU - Luo , Zhaofu AU - Hong , Xiaochun JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 193 EP - 207 PY - 2021 DA - 2021/04 SN - 3 DO - http://doi.org/10.12150/jnma.2021.193 UR - https://global-sci.org/intro/article_detail/jnma/18786.html KW - $D(m, n)$ system, Solitary wave solution, Periodic wave solution, Compacton, Peakon. AB -

In this paper, we employ the theory of the planar dynamical system to investigate the dynamical behavior and bifurcations of solutions of the traveling systems of the $D(m,n)$ equation. On the basis of the previous work of the reference [17], we obtain the solitary cusp waves solutions (peakons and valleyons), breaking wave solutions (compactons) and other periodic cusp wave solutions. Morever, we make a summary of exact traveling wave solutions to the $D(m,n)$ system including all the solutions which have been found from the references [4, 14, 17].

Cheng , RonghuaLuo , Zhaofu and Hong , Xiaochun. (2021). Bifurcations and New Traveling Wave Solutions for the Nonlinear Dispersion Drinfel'd-Sokolov ($D(m,n)$) System. Journal of Nonlinear Modeling and Analysis. 3 (2). 193-207. doi:10.12150/jnma.2021.193
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