Schrödinger equations on compact symmetric spaces and Gauss sums

2019 ◽  
Author(s):  
Tomoyuki Kakehi
Keyword(s):  
Symmetric Spaces ◽  
Gauss Sums ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Compact Symmetric Spaces

NONLINEAR SCHRÖDINGER EQUATIONS ON SUPER SYMMETRIC SPACES RELATED TO LIE SUPERALGEBRAS A(m, n)

1991 ◽  
Vol 06 (26) ◽  
pp. 4655-4666 ◽  
Author(s):  
AHMET CANOḠLU ◽  
BAHRİ GÜLDOḠAN ◽  
SELÂMİ SALİHOḠLU
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symmetric Spaces ◽  
Nonlinear Partial Differential Equations ◽  
Lie Superalgebras ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

We obtain new integrable coupled nonlinear partial differential equations by assuming that the soliton connection has values in the Lie superalgebras A(m, n). These equations are coupled nonlinear Schrödinger equations on various super symmetric spaces.

Schrödinger equations on locally symmetric spaces

2017 ◽  
Vol 371 (3-4) ◽  
pp. 1351-1374 ◽  
Author(s):  
A. Fotiadis ◽  
N. Mandouvalos ◽  
M. Marias
Keyword(s):  
Symmetric Spaces ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Locally Symmetric Spaces

NONLINEAR SCHRÖDINGER EQUATIONS ON SUPER SYMMETRIC SPACES RELATED TO ORTHOGONAL-SYMPLECTIC LIE SUPERALGEBRAS

1992 ◽  
Vol 07 (29) ◽  
pp. 7287-7304 ◽  
Author(s):  
AHMET CANOGLU ◽  
BAHRI GÜLDOGAN ◽  
SELÂMI SALIHOGLU
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symmetric Spaces ◽  
Nonlinear Partial Differential Equations ◽  
Lie Superalgebras ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

We obtain new integrable coupled nonlinear partial differential equations by assuming the soliton connection having values in orthogonal-symplectic Lie superalgebras [B(m, n), C(n), D(m, n)]. These equations are coupled Nonlinear Schrödinger equations on various super symmetric spaces.

scholarly journals Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Nakao Hayashi ◽  
Chunhua Li ◽  
Pavel I. Naumkin
Keyword(s):  
Lower Bound ◽  
Positive Root ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Time Decay ◽  
Large Initial Data ◽  
Initial Value ◽  
Optical Fields ◽  
Gauge Invariant ◽  
Dissipative Condition

We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearityλup-1uof orderpn<p≤1+2/nfor arbitrarily large initial data, where the lower boundpnis a positive root ofn+2p2-6p-n=0forn≥2andp1=1+2forn=1.Our purpose is to extend the previous results for higher space dimensions concerningL2-time decay and to improve the lower bound ofpunder the same dissipative condition onλ∈C:Im⁡ λ<0andIm⁡ λ>p-1/2pRe λas in the previous works.

Sign in / Sign up

Export Citation Format

Share Document