Universal Critical Power for Nonlinear Schroedinger Equations with a Symmetric Double Well Potential
- Faculty of Sciences, University of Modena e Reggio Emilia, Via Campi 213/B, I-41100 Modena (Italy)
Here we consider stationary states for nonlinear Schroedinger equations in any spatial dimension n with symmetric double well potentials. These states may bifurcate as the strength of the nonlinear term increases and we observe two different pictures depending on the value of the nonlinearity power: a supercritical pitchfork bifurcation, and a subcritical pitchfork bifurcation with two asymmetric branches occurring as the result of saddle-node bifurcations. We show that in the semiclassical limit, or for a large barrier between the two wells, the first kind of bifurcation always occurs when the nonlinearity power is less than a critical value; in contrast, when the nonlinearity power is larger than such a critical value then we always observe the second scenario. The remarkable fact is that such a critical value is a universal constant in the sense that it does not depend on the shape of the double well potential and on the dimension n.
- OSTI ID:
- 21370807
- Journal Information:
- Physical Review Letters, Vol. 103, Issue 19; Other Information: DOI: 10.1103/PhysRevLett.103.194101; (c) 2009 The American Physical Society; ISSN 0031-9007
- Country of Publication:
- United States
- Language:
- English
Similar Records
Hopf bifurcation and plasma instabilities
Symmetric and asymmetric solitons trapped in H-shaped potentials