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Volume 5, Issue 3
Bifurcations and Exact Solutions of the Gerdjikov-Ivanov Equation

Jinsen Zhuang, Yan Zhou & Jibin Li

DOI: 10.12150/jnma.2023.549

J. Nonl. Mod. Anal., 5 (2023), pp. 549-564.

Published online: 2023-08

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

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  • Abstract

For the Gerdjikov-Ivanov equation, by using the method of dynamical system, this paper investigates the exact explicit solutions with the form $q(x, t) = \phi(\xi) {\rm exp} [i(\kappa x-\omega t +\theta(\xi)],\xi= x-ct.$ In the given parameter regions, more than 14 explicit exact parametric representations are presented.

  • Keywords

Bifurcation, exact solution, planar Hamiltonian system, Gerdjikov-Ivanov equation.

  • AMS Subject Headings

34C23, 35Q51, 35Q52, 35Q53, 58J55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-549, author = {Zhuang , JinsenZhou , Yan and Li , Jibin}, title = {Bifurcations and Exact Solutions of the Gerdjikov-Ivanov Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {3}, pages = {549--564}, abstract = {

For the Gerdjikov-Ivanov equation, by using the method of dynamical system, this paper investigates the exact explicit solutions with the form $q(x, t) = \phi(\xi) {\rm exp} [i(\kappa x-\omega t +\theta(\xi)],\xi= x-ct.$ In the given parameter regions, more than 14 explicit exact parametric representations are presented.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.549}, url = {http://global-sci.org/intro/article_detail/jnma/21951.html} }
TY - JOUR T1 - Bifurcations and Exact Solutions of the Gerdjikov-Ivanov Equation AU - Zhuang , Jinsen AU - Zhou , Yan AU - Li , Jibin JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 549 EP - 564 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.549 UR - https://global-sci.org/intro/article_detail/jnma/21951.html KW - Bifurcation, exact solution, planar Hamiltonian system, Gerdjikov-Ivanov equation. AB -

For the Gerdjikov-Ivanov equation, by using the method of dynamical system, this paper investigates the exact explicit solutions with the form $q(x, t) = \phi(\xi) {\rm exp} [i(\kappa x-\omega t +\theta(\xi)],\xi= x-ct.$ In the given parameter regions, more than 14 explicit exact parametric representations are presented.

Jinsen Zhuang, Yan Zhou & Jibin Li. (2023). Bifurcations and Exact Solutions of the Gerdjikov-Ivanov Equation. Journal of Nonlinear Modeling and Analysis. 5 (3). 549-564. doi:10.12150/jnma.2023.549
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