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.

scholarly journals Rogue periodic waves of the focusing nonlinear Schrödinger equation

2018 ◽  
Vol 474 (2210) ◽  
pp. 20170814 ◽  
Author(s):  
Jinbing Chen ◽  
Dmitry E. Pelinovsky
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Elliptic Functions ◽  
Nonlinear Schrodinger Equation ◽  
Periodic Waves ◽  
Jacobian Elliptic Functions ◽  
Nonlinear Schrödinger

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov–Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine’s breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

scholarly journals Optical singular and dark solitons to the nonlinear Schrodinger equation in magneto-optic waveguides with anti-cubic nonlinearity.

2021 ◽  
Author(s):  
Thilagarajah Mathanaranjan ◽  
Hadi Rezazadeh ◽  
Mehmet Senol ◽  
Lanre Akinyemi
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Modified Simple Equation Method ◽  
Exact Soliton Solutions ◽  
Magneto Optic

Abstract The present paper aims to investigate the coupled nonlinear Schrodinger equation (NLSE) in magneto-optic waveguides having anti-cubic (AC) law nonlinearity. The solitons secured to magneto-optic waveguides with AC law nonlinearity are extremely useful to fiber-optic transmission technology. Three constructive techniques, namely, the (G'/G)-expansion method, the modified simple equation method (MSEM), and the extended tanh-function method are utilized to find the exact soliton solutions of this model. Consequently, dark, singular and combined dark-singular soliton solutions are obtained. The behaviours of soliton solutions are presented by 3D and 2D plots.

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.

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