Multi-Soliton Solutions of a Derivative Nonlinear Schrödinger Equation

1980 ◽  
Vol 49 (2) ◽  
pp. 813-816 ◽  
Author(s):  
Akira Nakamura ◽  
Hsing-Hen Chen
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

Oblique nonlinear Alfvén waves in strongly magnetized beam plasmas. Part 2. Soliton solutions and integrability

1993 ◽  
Vol 50 (3) ◽  
pp. 457-476 ◽  
Author(s):  
Bernard Deconinck ◽  
Peter Meuris ◽  
Frank Verheest
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Mhd Waves ◽  
Displacement Current ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

Oblique propagation of MHD waves in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation, and hence requires a new approach to solitary-wave solutions, integrability and related problems. The new equation is shown to be integrable by the use of the prolongation method, and by finding a sufficient number of conservation laws, and possesses bright and dark soliton solutions, besides possible periodic solutions.

DARBOUX TRANSFORMATION METHOD FOR GIVING SOLITON SOLUTIONS OF THE DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION

1989 ◽  
Vol 04 (16) ◽  
pp. 1573-1579 ◽  
Author(s):  
ZONG-YUN CHEN ◽  
NIAN-NING HUANG
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Transformation Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Jost Solutions

The so-called Darboux transformation method is presented for giving soliton solutions of the derivative nonlinear Schrödinger equation. With the help of the reduction transformation invariance, a possible form of the Darboux transformation is found simply. This method is more elementary and more simple as there is no need to discuss analyticities of the Jost solutions and time dependence of the scattering dates.

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