A Note on Exact Traveling Wave Solutions of the Perturbed Nonlinear Schrödinger's Equation with Kerr Law Nonlinearity

2012 ◽  
Vol 57 (5) ◽  
pp. 764-770 ◽  
Author(s):  
Zai-Yun Zhang ◽  
Xiang-Yang Gan ◽  
De-Min Yu ◽  
Ying-Hui Zhang ◽  
Xin-Ping Li
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Schrödinger’S Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Schrödinger's Equation ◽  
Nonlinear Schrodinger’S Equation ◽  
Nonlinear Schrödinger’S Equation

Abundant traveling wave solutions to the resonant nonlinear Schrödinger’s equation with variable coefficients

2020 ◽  
Vol 34 (12) ◽  
pp. 2050118 ◽  
Author(s):  
Hadi Rezazadeh ◽  
Kalim U. Tariq ◽  
Jamilu Sabi’u ◽  
Ahmet Bekir
Keyword(s):  
Traveling Wave ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
Mathematical Tool ◽  
Schrödinger’S Equation ◽  
Wave Solutions ◽  
Schrödinger's Equation ◽  
Nonlinear Schrodinger’S Equation ◽  
Nonlinear Schrödinger’S Equation

In this paper, some new traveling wave solutions to the resonant nonlinear Schrödinger’s equation (R-NLSE) with time-dependent coefficients are constructed. The well-known auxiliary equation method is applied to develop numerous interesting classes of nonlinearities, namely the Kerr law and parabolic law. Such approach provides an extensive mathematical tool to develop a family of traveling wave solutions such as bright, dark, singular and optical solutions to the nonlinear evolution model. Moreover, with the aid of symbolic computation the three-dimensional plot and contour plot have been carried out to demonstrate the dynamical behavior of the nonlinear complex model.

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