Self-similar solutions of certain coupled integrable systems

Self-similar solutions of certain coupled integrable systems

Similarity reductions of the coupled nonlinear Schrödinger equation and an integrable version of the coupled Maxwell-Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painlevé transcendents, leading to new exact self-similar solutions for these integrable equations. PACS numbers: 02.30.Ik., 02...

PERIODIC SOLUTIONS OF CERTAIN THREE DIMENSIONAL AUTONOMOUS SYSTEMS

There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...

Meromorphic Solutions to a Differential–difference Equation Describing Certain Self-similar Potentials

In this paper we prove the existence of meromorphic solutions to a nonlinear differential difference equation that describe certain self-similar potentials for the Schroedinger operator.

New Self - Similar Solutions of theNonlinear

Self-similar systems

Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Papers published in Hydrology and Earth System Sciences Discussions are under open-access review for the journal Hydrology and Earth System Sciences Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion EGU Abstract In many cases, the...