# On the steady-state solutions of a nonlinear photonic lattice model

## Abstract

In this paper, we consider the steady-state solutions of the following equation related with nonlinear photonic lattice model Δu=(Pu)/(1+|u|{sup 2}+|v|{sup 2}) +λu, Δv=(Qv)/(1+|u|{sup 2}+|v|{sup 2}) +λv, where u, v are real-value function defined on R/(τ{sub 1}Z) × R/(τ{sub 2}Z). The existence and non-existence of non-constant semi-trivial (with only one component zero) solutions are considered.

- Authors:

- School of Mathematics and LPMC, Nankai University, Tianjin 300071 (China)

- Publication Date:

- OSTI Identifier:
- 22403116

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS; FUNCTIONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; STEADY-STATE CONDITIONS

### Citation Formats

```
Liu, Chungen, E-mail: liucg@nankai.edu.cn, E-mail: tjftp@mail.nankai.edu.cn, and Ren, Qiang, E-mail: liucg@nankai.edu.cn, E-mail: tjftp@mail.nankai.edu.cn.
```*On the steady-state solutions of a nonlinear photonic lattice model*. United States: N. p., 2015.
Web. doi:10.1063/1.4914333.

```
Liu, Chungen, E-mail: liucg@nankai.edu.cn, E-mail: tjftp@mail.nankai.edu.cn, & Ren, Qiang, E-mail: liucg@nankai.edu.cn, E-mail: tjftp@mail.nankai.edu.cn.
```*On the steady-state solutions of a nonlinear photonic lattice model*. United States. doi:10.1063/1.4914333.

```
Liu, Chungen, E-mail: liucg@nankai.edu.cn, E-mail: tjftp@mail.nankai.edu.cn, and Ren, Qiang, E-mail: liucg@nankai.edu.cn, E-mail: tjftp@mail.nankai.edu.cn. Sun .
"On the steady-state solutions of a nonlinear photonic lattice model". United States.
doi:10.1063/1.4914333.
```

```
@article{osti_22403116,
```

title = {On the steady-state solutions of a nonlinear photonic lattice model},

author = {Liu, Chungen, E-mail: liucg@nankai.edu.cn, E-mail: tjftp@mail.nankai.edu.cn and Ren, Qiang, E-mail: liucg@nankai.edu.cn, E-mail: tjftp@mail.nankai.edu.cn},

abstractNote = {In this paper, we consider the steady-state solutions of the following equation related with nonlinear photonic lattice model Δu=(Pu)/(1+|u|{sup 2}+|v|{sup 2}) +λu, Δv=(Qv)/(1+|u|{sup 2}+|v|{sup 2}) +λv, where u, v are real-value function defined on R/(τ{sub 1}Z) × R/(τ{sub 2}Z). The existence and non-existence of non-constant semi-trivial (with only one component zero) solutions are considered.},

doi = {10.1063/1.4914333},

journal = {Journal of Mathematical Physics},

number = 3,

volume = 56,

place = {United States},

year = {Sun Mar 15 00:00:00 EDT 2015},

month = {Sun Mar 15 00:00:00 EDT 2015}

}

DOI: 10.1063/1.4914333

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