Painleve analysis and integrability of coupled non-linear Schrodinger equations

Sahadevan, R.; Tamizhmani, K. M.; Lakshmanan, M.

doi:10.1088/0305-4470/19/10/019

Cited by 117 publications

(46 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation (2) is found to be completely integrable derived in the process of solving by the inverse scattering transform (IST) by Zakharov and Schulman (see [1] and references therein) and then through systematic analysis of the Painlevé integrability [2] for more general constant coefficients' CNLS equation. When δ = 1, the aforementioned system (2) is a Manakov system [3], and bright and dark multisoliton solutions of the corresponding system have been derived with different procedures [3, 5 -7].…”

Section: The Similarity Transformationmentioning

confidence: 99%

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

Chen

2012

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

We systematically provide a similarity transformation reducing the (3 + 1)-dimensional inhomogeneous coupled nonlinear Schrödinger (CNLS) equation with variable coefficients and parabolic potential to the (1 + 1)-dimensional coupled nonlinear Schrödinger equation with constant coefficients. Based on the similarity transformation, we discuss the dynamics of the propagation of the three-dimensional bright-dark soliton, the interaction between two bright solitons, and the feature of the three-dimensional rogue wave with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

show abstract

Section: The Similarity Transformationmentioning

confidence: 99%

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

Chen

2012

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

show abstract

“…The analytical solutions and integrable classes of the CNLS equations have been a subject of intense investigations in recent years due to their rich variety of solutions [11,[14][15][16][17][18] . The Painlevé analysis is one of the most important methods discussing nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

A class of coupled nonlinear Schrödinger equations: Painlevé property, exact solutions, and application to atmospheric gravity waves

Liu

Sen-Yue

2010

Appl. Math. Mech.-Engl. Ed.

View full text Add to dashboard Cite

The Painlevé integrability and exact solutions to a coupled nonlinear Schrödin-ger (CNLS) equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painlevé test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

show abstract

“…The solutions of the coupled nonlinear Schrödinger equations (see Appendix 2) can be expressed in the form: y 1 (t) exp(iΩz), y 2 (t) exp(iΩz) where y 1 (t) and y 2 (t) are solutions to the Hamiltonian system with Hamiltonian (1) where Ω is an arbitrary constant. If α 1 = α 2 , β 1 = β 2 = β 3 = 1, γ 1 = γ 2 = γ 3 = 0, these equations are known to belong to the class of nonlinear evolution equations which are integrable by means of the inverse scattering method [21].…”

Section: Introductionmentioning

confidence: 99%