11 research outputs found
Transformations of ordinary differential equations via Darboux transformation technique
A new approach for obtaining the transformations of solutions of nonlinear
ordinary differential equations representable as the compatibility condition of
the overdetermined linear systems is proposed. The corresponding
transformations of the solutions of the overdetermined linear systems are
derived in the frameworks of the Darboux transformation technique.Comment: 7 pages, LaTeX2
Von Neumann equations with time-dependent Hamiltonians and supersymmetric quantum mechanics
Starting with a time-independent Hamiltonian and an appropriately chosen
solution of the von Neumann equation we construct
its binary-Darboux partner and an exact scattering solution of
where is time-dependent and not
isospectral to . The method is analogous to supersymmetric quantum mechanics
but is based on a different version of a Darboux transformation. We illustrate
the technique by the example where corresponds to a 1-D harmonic
oscillator. The resulting represents a scattering of a soliton-like
pulse on a three-level system.Comment: revtex, 3 eps file
Travelling solitons in the parametrically driven nonlinear Schroedinger equation
We show that the parametrically driven nonlinear Schroedinger equation has
wide classes of travelling soliton solutions, some of which are stable. For
small driving strengths nonpropogating and moving solitons co-exist while
strongly forced solitons can only be stably when moving sufficiently fast.Comment: The paper is available as the JINR preprint E17-2000-147(Dubna,
Russia) and the preprint of the Max-Planck Institute for the Complex Systems
mpipks/0009011, Dresden, Germany. It was submitted to Physical Review
NEUROHUMORAL ASPECTS OF FORMATION OF COR PULMONALE IN CHRONIC OBSTRUCTIVE PULMONARY DISEASES
Neurohumoral aspects of formation of cor pulmonale in chronic obstructive pulmonary diseases