TY - JOUR

T1 - Modulational instability and breathing motion in the two-dimensional nonlinear Schrödinger equation with a one-dimensional harmonic potential

AU - Sakaguchi, Hidetsugu

AU - Kageyama, Yusuke

PY - 2013/11/18

Y1 - 2013/11/18

N2 - Modulational instability and breathing motion are studied in the two-dimensional nonlinear Schrödinger (NLS) equation trapped by the one-dimensional harmonic potential. The trapping potential is uniform in the y direction and the wave function is confined in the x direction. A breathing motion appears when the initial condition is close to a stationary solution which is uniform in the y direction. The amplitude of the breathing motion is larger in the two-dimensional system than that in the corresponding one-dimensional system. Coupled equations of the one-dimensional NLS equation and two variational parameters are derived by the variational approximation to understand the amplification of the breathing motion qualitatively. On the other hand, there is a breathing solution in the x direction which is uniform in the y direction to the two-dimensional NLS equation. It is shown that the modulational instability along the y direction is suppressed when the breathing motion is sufficiently strong, even if the norm is above the critical value of the collapse.

AB - Modulational instability and breathing motion are studied in the two-dimensional nonlinear Schrödinger (NLS) equation trapped by the one-dimensional harmonic potential. The trapping potential is uniform in the y direction and the wave function is confined in the x direction. A breathing motion appears when the initial condition is close to a stationary solution which is uniform in the y direction. The amplitude of the breathing motion is larger in the two-dimensional system than that in the corresponding one-dimensional system. Coupled equations of the one-dimensional NLS equation and two variational parameters are derived by the variational approximation to understand the amplification of the breathing motion qualitatively. On the other hand, there is a breathing solution in the x direction which is uniform in the y direction to the two-dimensional NLS equation. It is shown that the modulational instability along the y direction is suppressed when the breathing motion is sufficiently strong, even if the norm is above the critical value of the collapse.

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U2 - 10.1103/PhysRevE.88.053203

DO - 10.1103/PhysRevE.88.053203

M3 - Article

AN - SCOPUS:84889249231

SN - 1539-3755

VL - 88

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 5

M1 - 053203

ER -