In this paper, we prove that the solution curve of the ground/positive bound states of a two-component Bose-Einstein condensate undergoes supercritical pitchfork bifurcations at some finite values of the inter-component scattering length. The ground state solutions bifurcate into two symmetric solutions with respect to some suitable axis on the symmetric domain, when a two-component BEC has equ...

We consider semilinear parabolic equations of the form ut = uxx + f(u), x ∈ R, t ∈ I, (A) where I = (0,∞) or I = (−∞,∞). Solutions defined for all (x, t) ∈ R2 are referred to as entire solutions. Assuming that f ∈ C1(R) is of a bistable type with stable constant steady states 0 and γ > 0, we show the existence of an entire solution U(x, t) of the following form. For t ≈ −∞, U(·, t) has two hump...

In this paper two fundamental questions in the contracted Schrödinger equation ~CSE! approach are considered by using Lipkin’s quasispin model: 1-1 mapping between the second-order reduced density matrix ~2-RDM! and the wave function of an excited state, and the uniqueness of the solution of CSE under incomplete N-representability conditions. We present some examples of the wave functions that ...

We show that polarization dependent string-string scattering provides new evidence for the identification of the Dabholkar-Harvey (DH) string solution with the heterotic string itself. First, we construct excited versions of the DH solution which carry arbitrary leftmoving waves yet are annihilated by half the supersymmetries. These solutions correspond in a natural way to Bogomolny-bound-satur...

The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the SU(4) symmetric point by means of Bethe ansatz. Following Sutherland’s previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a SU(4) singlet. ...

We are concerned with the following nonlinear Schr\"odinger equation \begin{eqnarray*} \begin{aligned} \begin{cases} -\Delta u+\lambda u=f(u) \ {\rm in}\ \mathbb{R}^{2},\\ u\in H^{1}(\mathbb{R}^{2}),~~~ \int_{\mathbb{R}^2}u^2dx=\rho, \end{cases} \end{aligned} \end{eqnarray*} where $\rho>0$ is given, $\lambda\in\mathbb{R}$ arises as a Lagrange multiplier and $f$ satisfies an exponential critical...