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Volume 10, Issue 4
Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

Chun-Yan Qin, Shou-Fu Tian, Li Zou & Wen-Xiu Ma

DOI: 10.4208/aamm.OA-2017-0220

Adv. Appl. Math. Mech., 10 (2018), pp. 948-977.

Published online: 2018-07

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  • Abstract

A (3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation is considered, which can be used to describe many nonlinear phenomena in plasma physics. By virtue of binary Bell polynomials, a bilinear representation of the equation is succinctly presented. Based on its bilinear formalism, we construct soliton solutions and Riemann theta function periodic wave solutions. The relationships between the soliton solutions and the periodic wave solutions are strictly established and the asymptotic behaviors of the Riemann theta function periodic wave solutions are analyzed with a detailed proof.

  • Keywords

A (3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation, Bell polynomial, solitary wave solution, periodic wave solution, asymptotic behavior.

  • AMS Subject Headings

35Q51,35Q53, 35C99, 68W30, 74J35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-948, author = {Qin , Chun-YanTian , Shou-FuZou , Li and Ma , Wen-Xiu}, title = {Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {4}, pages = {948--977}, abstract = {

A (3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation is considered, which can be used to describe many nonlinear phenomena in plasma physics. By virtue of binary Bell polynomials, a bilinear representation of the equation is succinctly presented. Based on its bilinear formalism, we construct soliton solutions and Riemann theta function periodic wave solutions. The relationships between the soliton solutions and the periodic wave solutions are strictly established and the asymptotic behaviors of the Riemann theta function periodic wave solutions are analyzed with a detailed proof.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0220}, url = {http://global-sci.org/intro/article_detail/aamm/12504.html} }
TY - JOUR T1 - Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation AU - Qin , Chun-Yan AU - Tian , Shou-Fu AU - Zou , Li AU - Ma , Wen-Xiu JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 948 EP - 977 PY - 2018 DA - 2018/07 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2017-0220 UR - https://global-sci.org/intro/article_detail/aamm/12504.html KW - A (3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation, Bell polynomial, solitary wave solution, periodic wave solution, asymptotic behavior. AB -

A (3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation is considered, which can be used to describe many nonlinear phenomena in plasma physics. By virtue of binary Bell polynomials, a bilinear representation of the equation is succinctly presented. Based on its bilinear formalism, we construct soliton solutions and Riemann theta function periodic wave solutions. The relationships between the soliton solutions and the periodic wave solutions are strictly established and the asymptotic behaviors of the Riemann theta function periodic wave solutions are analyzed with a detailed proof.

Qin , Chun-YanTian , Shou-FuZou , Li and Ma , Wen-Xiu. (2018). Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation. Advances in Applied Mathematics and Mechanics. 10 (4). 948-977. doi:10.4208/aamm.OA-2017-0220
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