The interaction of W-shaped rational solitons with kink wave for the nonlinear Schrödinger equation with anti-cubic nonlinearity

2020 ◽  
Vol 34 (12) ◽  
pp. 2050122 ◽  
Author(s):  
Iftikhar Ahmed ◽  
A. R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Symbolic Computation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Logarithmic Transformation ◽  
Cubic Nonlinearity ◽  
Nonlinear Schrödinger ◽  
Kink Wave

By utilizing the logarithmic transformation and symbolic computation with ansatz functions technique, W-shaped rational solitons are obtained for the nonlinear Schrödinger equation with anti-cubic nonlinearity. Meanwhile, the interaction between rational solitons and the kink wave is also investigated.

Peregrine-like rational solitons and their interaction with kink wave for the resonance nonlinear Schrödinger equation with Kerr law of nonlinearity

2019 ◽  
Vol 33 (24) ◽  
pp. 1950292 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Iftikhar Ahmed
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Symbolic Computation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Logarithmic Transformation ◽  
Nonlinear Schrödinger ◽  
Kerr Law ◽  
Kink Wave

By utilizing the logarithmic transformation and symbolic computation with ansatz functions technique, Peregrine-like rational solitons are obtained for the resonance nonlinear Schrödinger equation (R-NLSE) with Kerr law of nonlinearity. Meanwhile, the interaction between rational solitons and the kink wave is also investigated. The dynamics and many important properties of these obtained solutions are analyzed and briefly described in figures by selecting the appropriate parametric values.

NEW ENVELOPE SOLUTIONS FOR COMPLEX NONLINEAR SCHRÖDINGER+ EQUATION VIA SYMBOLIC COMPUTATION

2003 ◽  
Vol 14 (02) ◽  
pp. 225-235 ◽  
Author(s):  
ZHEN-YA YAN
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Symbolic Computation ◽  
Schrodinger Equation ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Jacobian Elliptic Functions ◽  
Nonlinear Schrödinger ◽  
Trigonometric Function Solutions

With the aid of symbolic computation, an extended Jacobian elliptic function expansion method is further extended to the complex nonlinear Schrödinger + equation. As a result, 24 families of the envelope doubly-periodic solutions with Jacobian elliptic functions are obtained. When the modulus m → 1 or zero, the corresponding six envelope solitary wave solutions and six envelope singly-periodic (trigonometric function) solutions are also found. This powerful method can also be applied to other equations, such as the nonlinear Schrödinger equation and Zakharov equation.

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