Lax pair, interactions and conversions of the nonlinear waves for a (2+1)-dimensional nonlinear Schrödinger equation in a Heisenberg ferromagnetic spin chain

2021 ◽  
Vol 136 (7) ◽  
Author(s):  
Xia-Xia Du ◽  
Bo Tian ◽  
He-Yuan Tian ◽  
Yan Sun
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Nonlinear Waves ◽  
Spin Chain ◽  
Schrodinger Equation ◽  
Lax Pair ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Pair Interactions

scholarly journals QUANTUM RESOLUTION OF THE NONLINEAR SUPER-SCHRÖDINGER EQUATION

2004 ◽  
Vol 19 (10) ◽  
pp. 1559-1577 ◽  
Author(s):  
V. CAUDRELIER ◽  
E. RAGOUCY
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Lax Pair ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Yangian Symmetry

We introduce a ℤ2-graded version of the nonlinear Schrödinger equation that includes one fermion and one boson at the same time. This equation is shown to possess a supersymmetry which proves to be itself part of a super-Yangian symmetry based on gl (1|1). The solution exhibits a super version form of the classical Rosales solution. Then, we second quantize these results, and give a Lax pair formulation (based on gl (2|1)) for the model.

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