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

Jianli Liang | Zendy; Jibin Li | Zendy

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

Author(s) -

Jianli Liang,

Jibin Li

Publication year - 2018

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2018.1194

Subject(s) - homoclinic orbit , phase portrait , peakon , nonlinear system , bounded function , mathematical analysis , mathematics , hamiltonian system , planar , nonlinear schrödinger equation , physics , bifurcation , schrödinger equation , quantum mechanics , integrable system , computer graphics (images) , computer science

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).

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