Symmetrically coupled higher-order nonlinear Schroedinger equations: singularity analysis and integrability

Abstract

The integrability of a system of two symmetrically coupled higher-order nonlinear Schrödinger equations with parameter coefficients is tested by means of the singularity analysis. It is proven that the system passes the Painlevé test for integrability only in ten distinct cases, of which two are new. For one of the new cases, a Lax pair and a multi-field generalization are obtained; for the other one, the equations of the system are uncoupled by a nonlinear transformation.

12 pages, LaTeX2e, IOP style, final version, to appear in J.Phys.A:Math.Gen

References in corpus (5)

• Optical Solitary Waves in the Higher Order Nonlinear Schrodinger Equation
• The Coupled Modified Korteweg-de Vries Equations
• New integrable systems of derivative nonlinear Schrödinger equations with multiple components
• Painlevé analysis of the coupled nonlinear Schrödinger equation for polarized optical waves in an isotropic medium
• Complete integrability of derivative nonlinear Schrödinger-type equations

Cited by in corpus (16)

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• A new integrable generalization of the Korteweg - de Vries equation
• Integrable discretizations of derivative nonlinear Schroedinger equations
• Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I
• Classification of integrable polynomial vector evolution equations
• Direct Methods and Symbolic Software for Conservation Laws of Nonlinear Equations
• Painlev{é} singularity structure analysis of three component Gross-Pitaevskii type equations
• Perturbation theory for nearly integrable multi-component nonlinear PDEs
• A new Painleve-integrable equation possessing KdV-type solitons
• Painlevé test of coupled Gross-Pitaevskii equations
• Integrability of a generalized short pulse equation revisited
• Cole-Hopf Like Transformation for a Class of Coupled Nonlinear Schroedinger Equations
• On a 'Mysterious' Case of a Quadratic Hamiltonian
• Integrability of one bilinear equation: singularity analysis and dimension
• On integrability of a third-order complex nonlinear wave equation
• Gauge equivalence among quantum nonlinear many body systems