Solitary wave and quasi-periodic wave solutions to a (3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation. (English) Zbl 1488.35466
Summary: 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.
MSC:
| 35Q51 | Soliton equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C99 | Representations of solutions to partial differential equations |
| 68W30 | Symbolic computation and algebraic computation |
| 74J35 | Solitary waves in solid mechanics |
Keywords:
(3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation; Bell polynomial; solitary wave solution; periodic wave solution; asymptotic behaviorSoftware:
PDEBellIIReferences:
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