BIFURCATIONS AND EXACT SOLUTIONS OF NONLINEAR SCHR&#214;DINGER EQUATION WITH AN ANTI-CUBIC NONLINEARITY

Jianli Liang; Jibin Li

doi:10.11948/2018.1194

2018 Volume 8 Issue 4

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Jianli Liang, Jibin Li. BIFURCATIONS AND EXACT SOLUTIONS OF NONLINEAR SCHRÖDINGER EQUATION WITH AN ANTI-CUBIC NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2018, 8(4): 1194-1210. doi: 10.11948/2018.1194

Citation:

Jianli Liang, Jibin Li. BIFURCATIONS AND EXACT SOLUTIONS OF NONLINEAR SCHRÖDINGER EQUATION WITH AN ANTI-CUBIC NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2018, 8(4): 1194-1210. doi: 10.11948/2018.1194

BIFURCATIONS AND EXACT SOLUTIONS OF NONLINEAR SCHRÖDINGER EQUATION WITH AN ANTI-CUBIC NONLINEARITY

Jianli Liang¹,
Jibin Li^1,2

1 School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
2 Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

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Abstract

Abstract

In this paper, we consider the nonlinear Schrödinger equation with an anti-cubic nonlinearity. By using the method of dynamical systems, we obtain bifurcations of the phase portraits of the corresponding planar dynamical system under different parameter conditions. Corresponding to different level curves defined by the Hamiltonian, we derive all exact explicit parametric representations of the bounded solutions (including periodic peakon solutions, periodic solutions, homoclinic solutions, heteroclinic solutions and compacton solutions).
- Periodic solution /
- periodic peakon /
- compacton solution /
- bifurcation /
- homoclinic solution /
- nonlinear Schrödinger equation with an anti-cubic nonlinearity
MSC: 34C37;34C23;74J30

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