### Electronic Research Archive

2021, Issue 4: 2561-2597. doi: 10.3934/era.2021002

# Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system

• Received: 01 August 2020 Revised: 01 November 2020 Published: 11 January 2021
• Primary: 35Q41, 35J50; Secondary: 35J10, 35Q55

• In this paper, we study a couple of NLS equations characterized by mixed cubic and super-linear sub-cubic power laws. Classification as well as existence and uniqueness of the steady state solutions have been investigated. Numerical simulations have been also provided illustrating graphically the theoretical results. Such simulations showed that possible chaotic behaviour seems to occur and needs more investigations.

Citation: Riadh Chteoui, Abdulrahman F. Aljohani, Anouar Ben Mabrouk. Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system[J]. Electronic Research Archive, 2021, 29(4): 2561-2597. doi: 10.3934/era.2021002

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• In this paper, we study a couple of NLS equations characterized by mixed cubic and super-linear sub-cubic power laws. Classification as well as existence and uniqueness of the steady state solutions have been investigated. Numerical simulations have been also provided illustrating graphically the theoretical results. Such simulations showed that possible chaotic behaviour seems to occur and needs more investigations.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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