| Volume 8, Number 1, 2018, Pages 250-271 DOI：10.11948/2018.250 |
| Dynamical behaviour and exact solutions of thirteenth order derivative nonlinear Schr\"{o}dinger equation |
| Temesgen Desta Leta,Jibin Li |
| Keywords:Coupled integrable system, exact solution, thirteenth order derivative nonlinear Schr\"{o}dinger equation, homoclinic orbits, hetroclinic orbits, periodic orbits. |
| Abstract: |
| In this paper, we considered the model of the thirteenth order derivatives of nonlinear Schr\"{o}dinger equations. It is shown that a wave packet ansatz inserted into these equations leads to an integrable Hamiltonian dynamical sub-system. By using bifurcation theory of planar dynamical systems, in different parametric regions, we determined the phase portraits. In each of these parametric regions we obtain possible exact explicit parametric representation of the traveling wave solutions corresponding to homoclinic, hetroclinic and periodic orbits. |
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