Volume 24, Issue 4
Ground States and Energy Asymptotics of the Nonlinear Schrödinger Equation with a General Power Nonlinearity

Xinran Ruan & Wenfan Yi

Commun. Comput. Phys., 24 (2018), pp. 1121-1142.

Published online: 2018-06

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  • Abstract

We study analytically the existence and uniqueness of the ground state of the nonlinear Schrödinger equation (NLSE) with a general power nonlinearity described by the power index σ≥0. For the NLSE under a box or a harmonic potential, we can derive explicitly the approximations of the ground states and their corresponding energy and chemical potential in weak or strong interaction regimes with a fixed nonlinearity σ. Besides, we study the case where the nonlinearity σ→∞ with a fixed interaction strength. In particular, a bifurcation in the ground states is observed. Numerical results in 1D and 2D will be reported to support our asymptotic results.

  • Keywords

Nonlinear Schrödinger equation, ground state, energy asymptotics, repulsive interaction.

  • AMS Subject Headings

35B40, 35P30, 35Q55, 65N25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-1121, author = {}, title = {Ground States and Energy Asymptotics of the Nonlinear Schrödinger Equation with a General Power Nonlinearity}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {4}, pages = {1121--1142}, abstract = {

We study analytically the existence and uniqueness of the ground state of the nonlinear Schrödinger equation (NLSE) with a general power nonlinearity described by the power index σ≥0. For the NLSE under a box or a harmonic potential, we can derive explicitly the approximations of the ground states and their corresponding energy and chemical potential in weak or strong interaction regimes with a fixed nonlinearity σ. Besides, we study the case where the nonlinearity σ→∞ with a fixed interaction strength. In particular, a bifurcation in the ground states is observed. Numerical results in 1D and 2D will be reported to support our asymptotic results.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2018.hh80.02}, url = {http://global-sci.org/intro/article_detail/cicp/12321.html} }
TY - JOUR T1 - Ground States and Energy Asymptotics of the Nonlinear Schrödinger Equation with a General Power Nonlinearity JO - Communications in Computational Physics VL - 4 SP - 1121 EP - 1142 PY - 2018 DA - 2018/06 SN - 24 DO - http://dor.org/10.4208/cicp.2018.hh80.02 UR - https://global-sci.org/intro/cicp/12321.html KW - Nonlinear Schrödinger equation, ground state, energy asymptotics, repulsive interaction. AB -

We study analytically the existence and uniqueness of the ground state of the nonlinear Schrödinger equation (NLSE) with a general power nonlinearity described by the power index σ≥0. For the NLSE under a box or a harmonic potential, we can derive explicitly the approximations of the ground states and their corresponding energy and chemical potential in weak or strong interaction regimes with a fixed nonlinearity σ. Besides, we study the case where the nonlinearity σ→∞ with a fixed interaction strength. In particular, a bifurcation in the ground states is observed. Numerical results in 1D and 2D will be reported to support our asymptotic results.

Xinran Ruan & Wenfan Yi. (2020). Ground States and Energy Asymptotics of the Nonlinear Schrödinger Equation with a General Power Nonlinearity. Communications in Computational Physics. 24 (4). 1121-1142. doi:10.4208/cicp.2018.hh80.02
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