| Citation: |
M. E. Elbrolosy, A. A. Elmandouh. CONSTRUCTION OF NEW TRAVELING WAVE SOLUTIONS FOR THE (2+1) DIMENSIONAL EXTENDED KADOMTSEV-PETVIASHVILI EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 533-550. doi: 10.11948/20210195
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CONSTRUCTION OF NEW TRAVELING WAVE SOLUTIONS FOR THE (2+1) DIMENSIONAL EXTENDED KADOMTSEV-PETVIASHVILI EQUATION
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Abstract
This work is interested in constructing traveling wave solutions for the (2+1)-dimensional extended Kadomtsev–Petviashvili equation that is utilized as a model for the surface waves and internal waves in straits or channels. Based on the bifurcation analysis of the traveling wave system, we use the conserved quantity to construct some new bounded traveling wave solutions such as periodic and solitary solutions in addition to some unbounded novel wave solutions. Some of the new solutions and their corresponding orbits are clarified graphically. Moreover, we examine numerically the dynamical behaviour for the perturbed (2+1)-dimensional extended Kadomtsev–Petviashvili equation by adding a perturbed periodic term.
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References
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M. E. Elbrolosy, A. A. Elmandouh. CONSTRUCTION OF NEW TRAVELING WAVE SOLUTIONS FOR THE (2+1) DIMENSIONAL EXTENDED KADOMTSEV-PETVIASHVILI EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 533-550. doi: 10.11948/20210195
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- Figure 1. Phase portrait for the planar dynamical system (2.5). The solid circles indicate to the equilibrium points.
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Figure 2. Bifurcation boundary on the
$ k\rho $ -plane for a fixed value of$ \gamma $ . - Figure 3. Graphic representations for the periodic solution (3.5).
- Figure 4. Graphic representations for the solution (3.14).
- Figure 5. Graphic representations for the solitary solution (3.7).
- Figure 6. Graphic representations for the solution (3.17).
- Figure 7. Graphic representations for the solution (3.10).
- Figure 8. Graphic representations for the solution (3.9).
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Figure 9. Phase portrait for the dynamical system (5.3) when
$ k=1, p=-0.05, q=2, \rho=-1, \gamma=1 $ , and$ \psi(0)=0.05, z(0)=0.05 $ . -
Figure 10. Phase portrait for the dynamical system (5.3) when
$ k=0.04, p=5, q=0.05, \rho=4, \gamma=2 $ , and$ \psi(0)=0.05, z(0)=1 $ .