scholarly journals Higher Conservation Laws for the Nonlinear Schrodinger Equation through Backlund Transformation

1975 ◽  
Vol 53 (2) ◽  
pp. 585-586 ◽  
Author(s):  
J. Satsuma
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bäcklund Transformation ◽  
Nonlinear Schrodinger Equation ◽  
Backlund Transformation ◽  
Nonlinear Schrödinger

General variable separation solution and new localized excitations for the (2 + 1)-dimensional nonlinear Schrödinger equation

2006 ◽  
Vol 84 (12) ◽  
pp. 1107-1123
Author(s):  
Cheng -Lin Bai ◽  
Hai -Quan Hu ◽  
Wen -Jun Wang ◽  
Hong Zhao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bäcklund Transformation ◽  
Nonlinear Schrodinger Equation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Nonlinear Schrödinger ◽  
New Class ◽  
Localized Excitations

By applying a special Bäcklund transformation, a general variable separation solution for the (2 + 1)-dimensional nonlinear Schrödinger equation is derived. In addition to some types of the usual localized excitations, such as dromions, lumps, ring solitons, oscillated dromions, and breathers, soliton structures can be easily constructed by selecting arbitrary functions appropriately. A new class of localized excitations, like fractal-dromions, fractal-lumps, peakons, compactons, and folded excitations of this system is found by selecting appropriate functions. Some interesting novel features of these structures are revealed.PACS Nos.: 05.45.–a, 02.30.Jr

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