Nonlinearizations of spectral problems of the nonlinear Schrödinger equation and the real-valued modified Korteweg–de Vries equation

2007 ◽  
Vol 48 (1) ◽  
pp. 013510 ◽  
Author(s):  
Ruguang Zhou
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Vries Equation ◽  
Nonlinear Schrodinger Equation ◽  
The Real ◽  
Nonlinear Schrödinger ◽  
Spectral Problems ◽  
De Vries

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).

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