Physics – Mathematical Physics
Scientific paper
2010-10-12
Physics
Mathematical Physics
22 pages, 1 figure
Scientific paper
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave evolution in external fields with variable quadratic potentials is totally determined by the linear problem, like motion of a classical particle with acceleration, and the (self-similar) soliton shape is due to a subtle balance between the linear Hamiltonian (dispersion and potential) and nonlinearity in the Schroedinger equation by the standards of soliton theory. Most linear (hypergeometric, Bessel) and a few nonlinear (Jacobian elliptic, second Painleve transcendental) classical special functions of mathematical physics are linked together through these solutions, thus providing a variety of nonlinear integrable cases. Examples include bright and dark solitons, and Jacobi elliptic and second Painleve transcendental solutions for several variable Hamiltonians that are important for current research in nonlinear optics and Bose-Einstein condensation. The Feshbach resonance matter wave soliton management is briefly discussed from this new perspective.
Suazo Erwin
Suslov Sergei K.
No associations
LandOfFree
Soliton-like Solutions for Nonlinear Schroedinger Equation with Variable Quadratic Hamiltonians does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Soliton-like Solutions for Nonlinear Schroedinger Equation with Variable Quadratic Hamiltonians, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Soliton-like Solutions for Nonlinear Schroedinger Equation with Variable Quadratic Hamiltonians will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-225862