Darboux transformations for super-Schrödinger equation, super-Dirac equation and their exact solutions

2017 ◽  
Vol 88 (2) ◽  
pp. 1257-1271 ◽  
Author(s):  
Fajun Yu ◽  
Lili Feng ◽  
Li Li
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Exact Solutions ◽  
Schrodinger Equation ◽  
Darboux Transformations

scholarly journals Iterants, Majorana Fermions and the Majorana-Dirac Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1373
Author(s):  
Louis H. Kauffman
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Clifford Algebras ◽  
Discrete Systems ◽  
Complex Numbers ◽  
Majorana Fermions ◽  
Matrix Algebras ◽  
Dirac Equations ◽  
Points Of View

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands.

scholarly journals Exact Solutions of the Generalized Nonlinear Schrodinger Equation

2021 ◽  
pp. 18-25
Author(s):  
Gaukhar Shaikhova ◽  
Arailym Syzdykova ◽  
Samgar Daulet
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Physical Problems ◽  
Different Types ◽  
Generalized Nonlinear Schrödinger Equation

In this work, the generalized nonlinear Schrodinger equation is investigated. Exact solutions are derived by the sinecosine method. This method is used to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The obtained solutions are found to be important for the explanation of some practical physical problems.

scholarly journals Complex PT -symmetric nonlinear Schrödinger equation and Burgers equation

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120059 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Wave ◽  
Schrodinger Equation ◽  
Wave Equations ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Wave Equations ◽  
Nonlinear Schrödinger

The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg–de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schrödinger equations (known as the Gross–Pitaevskii equation in Bose–Einstein condensates) with several complex -symmetric potentials. Finally, some complex -symmetric extension principles are used to generate some complex -symmetric nonlinear wave equations starting from both -symmetric (e.g. the KdV equation) and non- -symmetric (e.g. the Burgers equation) nonlinear wave equations. In particular, we discuss exact solutions of some representative ones of the complex -symmetric Burgers equation in detail.

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