scholarly journals Breather’s Properties within the Framework of the Modified Korteweg–de Vries Equation

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 638 ◽  
Author(s):  
Ekaterina Didenkulova ◽  
Efim Pelinovsky
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Vries Equation ◽  
Nonlinear Schrodinger Equation ◽  
Wave Shape ◽  
Cubic Nonlinearity ◽  
Envelope Soliton ◽  
De Vries ◽  
N Wave

We study a breather’s properties within the framework of the modified Korteweg–de Vries (mKdV) model, where cubic nonlinearity is essential. Extrema, moments, and invariants of a breather with different parameters have been analyzed. The conditions in which a breather moves in one direction or another has been determined. Two limiting cases have been considered: when a breather has an N-wave shape and can be interpreted as two solitons with different polarities, and when a breather contains many oscillations and can be interpreted as an envelope soliton of the nonlinear Schrödinger equation (NLS).

scholarly journals Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Chachou Samet ◽  
M. Benarous ◽  
M. Asad-uz-zaman ◽  
U. Al Khawaja
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Cubic Nonlinearity ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
Third Order Dispersion ◽  
Solitonic Solution ◽  
Order Dispersion

We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation. We establish the integrability condition for the most general nonlinear Schrödinger equation with cubic nonlinearity and discuss the effect of the coefficients of the higher-order terms in the solitonic solution. We find that the third-order dispersion term can be used to control the soliton motion without the need for an external potential. We discuss the integrability conditions and find the solitonic solution of some of the well-known nonlinear Schrödinger equations with cubic nonlinearity and time-dependent coefficients. We also investigate the higher-order nonlinear Schrödinger equation with cubic and quintic nonlinearities.

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.

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