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Volume 4, Issue 3
Dynamical Behavior and Exact Traveling Wave Solutions for Three Special Variants of the Generalized Tzitzeica Equation

Rongzheng Shu, Haohao Qian & Lina Zhang

DOI: 10.12150/jnma.2022.529

J. Nonl. Mod. Anal., 4 (2022), pp. 529-538.

Published online: 2022-06

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

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  • Abstract

The dynamics and bifurcations of traveling wave solutions are studied for three nonlinear wave equations. A new phenomenon, such as a composed orbit, which consists of two or three heteroclinic orbits, may correspond to a solitary wave solution, a periodic wave solution or a peakon solution, is found for the equations. Some previous results are extended.

  • Keywords

Generalized Tzitzeica equation, Solitary wave solution, Periodic wave solution, Peakon solution.

  • AMS Subject Headings

34C23, 37G10, 37G15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-529, author = {Shu , RongzhengQian , Haohao and Zhang , Lina}, title = {Dynamical Behavior and Exact Traveling Wave Solutions for Three Special Variants of the Generalized Tzitzeica Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {3}, pages = {529--538}, abstract = {

The dynamics and bifurcations of traveling wave solutions are studied for three nonlinear wave equations. A new phenomenon, such as a composed orbit, which consists of two or three heteroclinic orbits, may correspond to a solitary wave solution, a periodic wave solution or a peakon solution, is found for the equations. Some previous results are extended.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.529}, url = {http://global-sci.org/intro/article_detail/jnma/20723.html} }
TY - JOUR T1 - Dynamical Behavior and Exact Traveling Wave Solutions for Three Special Variants of the Generalized Tzitzeica Equation AU - Shu , Rongzheng AU - Qian , Haohao AU - Zhang , Lina JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 529 EP - 538 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.529 UR - https://global-sci.org/intro/article_detail/jnma/20723.html KW - Generalized Tzitzeica equation, Solitary wave solution, Periodic wave solution, Peakon solution. AB -

The dynamics and bifurcations of traveling wave solutions are studied for three nonlinear wave equations. A new phenomenon, such as a composed orbit, which consists of two or three heteroclinic orbits, may correspond to a solitary wave solution, a periodic wave solution or a peakon solution, is found for the equations. Some previous results are extended.

Shu , RongzhengQian , Haohao and Zhang , Lina. (2022). Dynamical Behavior and Exact Traveling Wave Solutions for Three Special Variants of the Generalized Tzitzeica Equation. Journal of Nonlinear Modeling and Analysis. 4 (3). 529-538. doi:10.12150/jnma.2022.529
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