EXTENDED SYMMETRIES AND SOLUTIONS OF (2 + 1)-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION WITH VARIABLE COEFFICIENTS

2009 ◽  
Vol 20 (11) ◽  
pp. 1681-1696
Author(s):  
JIA WANG ◽  
BIAO LI
Keyword(s):  
Symmetry Group ◽  
Schrodinger Equation ◽  
Variable Coefficients ◽  
Group Method ◽  
Nonlinear Schrödinger ◽  
Time Space ◽  
Generalized Symmetry ◽  
Nonlinear Schrodinger Equations ◽  
Constant Coefficients ◽  
Dimensional Variable

By generalized symmetry group method, some time-space-dependent finite transformations between two different (2 + 1)-dimensional nonlinear Schrödinger equations (NLSE) are constructed. From these transformations, some (2 + 1)-dimensional variable coefficients NLSE can be reduced to another variable coefficients NLSE or corresponding constant coefficients NLSE. Abundant solutions of some (2 + 1)-dimensional variable coefficients NLSE are obtained from their corresponding constant coefficients NLSE.

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

2012 ◽  
Vol 67 (8-9) ◽  
pp. 483-490 ◽  
Author(s):  
Junchao Chen ◽  
Biao Li
Keyword(s):  
Similarity Transformation ◽  
Rogue Wave ◽  
Three Dimensional ◽  
Dark Soliton ◽  
Variable Coefficients ◽  
Nonlinear Schrödinger ◽  
Time Space ◽  
Potential Applications ◽  
Constant Coefficients ◽  
Space Modulation

We systematically provide a similarity transformation reducing the (3+1)-dimensional inhomogeneous coupled nonlinear Schrodinger (CNLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional coupled nonlinear Schrodinger equation with constant coefficients. Based on the similarity transformation, we discuss the dynamics of the propagation of the three-dimensional bright-dark soliton, the interaction between two bright solitons, and the feature of the three-dimensional rogue wave with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

scholarly journals ASYMPTOTIC STABILITY OF NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL

2005 ◽  
Vol 17 (10) ◽  
pp. 1143-1207 ◽  
Author(s):  
ZHOU GANG ◽  
I. M. SIGAL
Keyword(s):  
Asymptotic Stability ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Nonlinear Schrodinger Equation ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Generalized Nonlinear Schrödinger Equation

We prove asymptotic stability of trapped solitons in the generalized nonlinear Schrödinger equation with a potential in dimension 1 and for even potential and even initial conditions.

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