Quantum oscillations between weakly coupled Bose–Einstein condensates: Evolution in a non-degenerate double well

In this paper, we discuss coherent atomic oscillations between two weakly coupled Bose–Einstein condensates that are energetically different. The weak link is notionally provided by a laser barrier in a (possibly asymmetric) multi-well trap or by Raman coupling between condensates in different hyperfine levels. The resultant boson Josephson junction dynamics is described by a double-well nonlinear Gross–Pitaevskii equation. On the basis of a new set of Jacobian elliptic function solutions, we describe the period of the oscillations as well as associated quantities and predict novel observable consequences of the interplay of the energy difference and initial phase difference between the two condensate populations.

Elliptic- and hyperbolic-function solutions of the nonlocal reverse-time and reverse-space-time nonlinear Schrödinger equations

In this paper, we obtain the stationary elliptic- and hyperbolic-function solutions of the nonlocal reverse-time and reverse-space-time nonlinear Schrödinger (NLS) equations based on their connection with the standard Weierstrass elliptic equation. The reverse-time NLS equation possesses the bounded dn-, cn-, sn-, sech-, and tanh-function solutions. Of special interest, the tanh-function solution can display both the dark- and antidark-soliton profiles. The reverse-space-time NLS equation admits the general Jacobian elliptic-function solutions (which are exponentially growing at one infinity or display the periodical oscillation in x), the bounded dn- and cn-function solutions, as well as the K-shifted dn- and sn-function solutions. At the degeneration, the hyperbolic-function solutions may exhibit an exponential growth behavior at one infinity, or show the gray- and bright-soliton profiles.

Analytical solutions of differential-difference sine-Gordon equation

In modern textile engineering, non-linear differential-difference equations are often used to describe some phenomena arising in heat/electron conduction and flow in carbon nanotubes. In this paper, we extend the variable coefficient Jacobian elliptic function method to solve non-linear differential-difference sine-Gordon equation by introducing a negative power and some variable coefficients in the ansatz, and derive two series of Jacobian elliptic function solutions. When the modulus of Jacobian elliptic function approaches to 1, some solutions can degenerate into some known solutions in the literature.

Extended Jacobian Elliptic Function Expansion Method and Its Applications in Mathematical Physics

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to some nonlinear evolution equations which play an important role inmathematical physics.

New Periodic Solutions for a Class of Zakharov Equations

Through applying the Jacobian elliptic function method, we obtain the periodic solution for a series of nonlinear Zakharov equations, which contain Klein-Gordon Zakharov equations, Zakharov equations, and Zakharov-Rubenchik equations.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.