Breather solutions of the integrable quintic nonlinear Schrödinger equation and their interactions

A. Chowdury; D. J. Kedziora; A. Ankiewicz; N. Akhmediev

doi:10.1103/PhysRevE.91.022919

Breather solutions of the integrable quintic nonlinear Schrödinger equation and their interactions

A. Chowdury, D. J. Kedziora, A. Ankiewicz, N. Akhmediev

Research output: Contribution to journal › Article › peer-review

104 Citations (Scopus)

Abstract

We present breather solutions of the quintic integrable equation of the Schrödinger hierarchy. This equation has terms describing fifth-order dispersion and matching nonlinear terms. Using a Darboux transformation, we derive first-order and second-order breather solutions. These include first- and second-order rogue-wave solutions. To some extent, these solutions are analogous with the corresponding nonlinear Schrödinger equation (NLSE) solutions. However, the presence of a free parameter in the equation results in specific solutions that have no analogues in the NLSE case. We analyze new features of these solutions.

Original language	English
Article number	022919
Journal	Physical Review E
Volume	91
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevE.91.022919
Publication status	Published - 24 Feb 2015

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10.1103/PhysRevE.91.022919

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abstract = "We present breather solutions of the quintic integrable equation of the Schr{\"o}dinger hierarchy. This equation has terms describing fifth-order dispersion and matching nonlinear terms. Using a Darboux transformation, we derive first-order and second-order breather solutions. These include first- and second-order rogue-wave solutions. To some extent, these solutions are analogous with the corresponding nonlinear Schr{\"o}dinger equation (NLSE) solutions. However, the presence of a free parameter in the equation results in specific solutions that have no analogues in the NLSE case. We analyze new features of these solutions.",

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N2 - We present breather solutions of the quintic integrable equation of the Schrödinger hierarchy. This equation has terms describing fifth-order dispersion and matching nonlinear terms. Using a Darboux transformation, we derive first-order and second-order breather solutions. These include first- and second-order rogue-wave solutions. To some extent, these solutions are analogous with the corresponding nonlinear Schrödinger equation (NLSE) solutions. However, the presence of a free parameter in the equation results in specific solutions that have no analogues in the NLSE case. We analyze new features of these solutions.

AB - We present breather solutions of the quintic integrable equation of the Schrödinger hierarchy. This equation has terms describing fifth-order dispersion and matching nonlinear terms. Using a Darboux transformation, we derive first-order and second-order breather solutions. These include first- and second-order rogue-wave solutions. To some extent, these solutions are analogous with the corresponding nonlinear Schrödinger equation (NLSE) solutions. However, the presence of a free parameter in the equation results in specific solutions that have no analogues in the NLSE case. We analyze new features of these solutions.

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Breather solutions of the integrable quintic nonlinear Schrödinger equation and their interactions

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