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Rogue waves, bright-dark solitons and traveling wave solutions of the \((3+1)\)-dimensional generalized Kadomtsev-Petviashvili equation. (English) Zbl 1420.35323
Summary: In this paper, a \((3+1)\)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation is investigated, which describes the dynamics of nonlinear waves in plasma physics and fluid dynamics. By employing the extended homoclinic test method, we construct a new family of two wave solutions, rational breather wave and rogue wave solutions of the equation. Moreover, by virtue of some ansatz functions and the Riccati equation method, its analytical bright soliton, dark soliton and traveling wave solutions are derived. Finally, we obtain its exact power series solution with the convergence analysis. In order to further understand the dynamics, we provide some graphical analysis of these solutions.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35C07 Traveling wave solutions
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