scholarly journals Bosonization, singularity analysis, nonlocal symmetry reductions and exact solutions of supersymmetric KdV equation

2013 ◽  
Vol 2013 (5) ◽  
Author(s):  
Xiao Nan Gao ◽  
S. Y. Lou ◽  
Xiao Yan Tang
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Singularity Analysis ◽  
Nonlocal Symmetry ◽  
Symmetry Reductions ◽  
Supersymmetric Kdv Equation

scholarly journals Recursion Operator and Local and Nonlocal Symmetries of a New Modified KdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Qian Suping ◽  
Li Xin
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Symmetry Algebra ◽  
Original Model ◽  
Identity Transformation ◽  
Recursion Operator ◽  
Nonlocal Symmetries ◽  
Symmetry Reductions ◽  
Finite Dimensional ◽  
Modified Kdv Equation

The recursion operator of a new modified KdV equation and its inverse are explicitly given. Acting the recursion operator and its inverse on the trivial symmetry 0 related to the identity transformation, the infinitely many local and nonlocal symmetries are obtained. Using a closed finite dimensional symmetry algebra with both local and nonlocal symmetries of the original model, some symmetry reductions and exact solutions are found.

SOLVING THE GENERALIZED BURGERS–KdV EQUATION BY A COMBINATION METHOD

2008 ◽  
Vol 22 (21) ◽  
pp. 2021-2025 ◽  
Author(s):  
YUANXI XIE
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Combination Method ◽  
Generalized Kdv Equation ◽  
Generalized Burgers Equation

In view of the analysis on the characteristics of the generalized Burgers equation, generalized KdV equation and generalized Burgers–KdV equation, a combination method is presented to seek the explicit and exact solutions to the generalized Burgers–KdV equation by combining with those of the generalized Burgers equation and generalized KdV equation. As a result, many explicit and exact solutions for the generalized Burgers–KdV equation are successfully obtained by this technique.

scholarly journals BI-HAMILTONIAN STRUCTURE OF THE SUPERSYMMETRIC NONLINEAR SCHRÖDINGER EQUATION

1995 ◽  
Vol 10 (27) ◽  
pp. 2019-2028 ◽  
Author(s):  
J.C. BRUNELLI ◽  
ASHOK DAS
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Hamiltonian Structure ◽  
Kdv Equation ◽  
Nonlinear Schrodinger Equation ◽  
Hamiltonian Reduction ◽  
Hamiltonian Structures ◽  
Nonlinear Schrödinger ◽  
Supersymmetric Kdv Equation

We show that the supersymmetric nonlinear Schrödinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two-boson hierarchy through a field redefinition. We also show how the two Hamiltonian structures of the supersymmetric KdV equation can also be derived from a Hamiltonian reduction of the supersymmetric two-boson hierarchy.

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