Infinite hierarchy of nonlinear Schrödinger equations and their solutions

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

doi:10.1103/PhysRevE.93.012206

Infinite hierarchy of nonlinear Schrödinger equations and their solutions

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

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

153 Citations (Scopus)

Abstract

We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

Original language	English
Article number	012206
Journal	Physical Review E
Volume	93
Issue number	1
DOIs	https://doi.org/10.1103/PhysRevE.93.012206
Publication status	Published - 11 Jan 2016

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abstract = "We study the infinite integrable nonlinear Schr{\"o}dinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that {"}even- order{"} equations in the set affect phase and {"}stretching factors{"} in the solutions, while {"}odd-order{"} equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.",

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AU - Kedziora, D. J.

AU - Chowdury, A.

AU - Bandelow, U.

AU - Akhmediev, N.

PY - 2016/1/11

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N2 - We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

AB - We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

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Infinite hierarchy of nonlinear Schrödinger equations and their solutions

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