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

Xinran Ruan & Wenfan Yi

DOI: 10.4208/cicp.2018.hh80.02

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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  • TXT
@Article{CiCP-24-1121, author = {Xinran Ruan and Wenfan Yi}, 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 AU - Xinran Ruan & Wenfan Yi JO - Communications in Computational Physics VL - 4 SP - 1121 EP - 1142 PY - 2018 DA - 2018/06 SN - 24 DO - http://doi.org/10.4208/cicp.2018.hh80.02 UR - https://global-sci.org/intro/article_detail/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 and Wenfan Yi. (2018). 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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