Generalized Darboux transformation and higher-order rogue wave solutions to the Manakov system
Abstract
In this paper, we construct a generalized recursive Darboux transformation of a focusing vector nonlinear Schrödinger equation known as the Manakov system. We apply this generalized recursive Darboux transformation to the Lax-pairs of this system in view of generating the Nth-order vector generalization rogue wave solutions with the same spectral parameter through a direct iteration rule. As a result, we discuss the first, second and third-order vector generalization rogue wave solutions while illustrating these features with some depictions. We show that higher-order rogue wave solutions depend on the values of their free parameters.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2016
- DOI:
- 10.48550/arXiv.1605.06132
- arXiv:
- arXiv:1605.06132
- Bibcode:
- 2016arXiv160506132M
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics;
- Nonlinear Sciences - Pattern Formation and Solitons;
- 37K10 (37M15)
- E-Print:
- 20 pages, 13 figures