Singular point analysis and integrals of motion for coupled nonlinear Schroedinger equations
Abstract
For a system of two coupled nonlinear Schroedinger equations and the corresponding Madelung fluid equations, the similarity transformation and reductions to ordinary differential equations are calculated. The symmetries can be used to classify several types of solutions. Besides a system of coupled Painleve II equations, a 2D quartic Hamiltonian system is obtained. Using Noether's theorem and performing a Painleve test, the parameters which lead to regular motion on tori are identified. Using the results of the Ptest, heretofore undiscovered integrals of motion for the Madelung fluid are obtained by direct calculations. Investigating the dynamics of the system for parameters that are different from those obtained by the Painleve test, the surface of section is calculated numerically and the transition into chaotic behavior is studied.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 August 1991
 DOI:
 10.1098/rspa.1991.0092
 Bibcode:
 1991RSPSA.434..263B
 Keywords:

 Chaos;
 Equations Of Motion;
 Nonlinear Equations;
 Schroedinger Equation;
 Similarity Theorem;
 Singularity (Mathematics);
 Hamiltonian Functions;
 Optimization;
 Fluid Mechanics and Heat Transfer