Ladder Operator Approach of Special Functions and the N-Soliton Solutions of the 2+1 Dimensional Finite Toda Equation

2004 ◽  
Vol 73 (4) ◽  
pp. 838-842 ◽  
Author(s):  
Akira Nakamura
Keyword(s):  
Special Functions ◽  
Soliton Solutions ◽  
Toda Equation ◽  
Operator Approach ◽  
Ladder Operator

On the Full-Discrete Extended Generalised q-Difference Toda System

2017 ◽  
Vol 72 (8) ◽  
pp. 703-709
Author(s):  
Chuanzhong Li ◽  
Anni Meng
Keyword(s):  
Difference Equation ◽  
Hamiltonian Structure ◽  
Soliton Solutions ◽  
Toda Equation ◽  
Lax Pairs ◽  
Toda System ◽  
Toda Hierarchy

AbstractIn this paper, we construct a full-discrete integrable difference equation which is a full-discretisation of the generalised q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of an extended generalised full-discrete q-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the extended full-discrete generalised q-Toda hierarchy are given.

Exact wavefunctions for free anyons: ladder operator approach

1992 ◽  
Vol 164 (1) ◽  
pp. 65-69 ◽  
Author(s):  
K.H. Cho ◽  
Chaiho Rim ◽  
D.S. Soh
Keyword(s):  
Operator Approach ◽  
Ladder Operator

scholarly journals The differential-q-difference 2D Toda equation: bilinear form and soliton solutions

2019 ◽  
Vol 1391 ◽  
pp. 012122
Author(s):  
B.B. Kutum ◽  
K.R. Yesmakhanova ◽  
G.N. Shaikhova
Keyword(s):  
Bilinear Form ◽  
Soliton Solutions ◽  
Toda Equation

scholarly journals Generalized binomial states: ladder operator approach

1996 ◽  
Vol 29 (17) ◽  
pp. 5637-5644 ◽  
Author(s):  
Hong-Chen Fu ◽  
Ryu Sasaki
Keyword(s):  
Operator Approach ◽  
Ladder Operator

scholarly journals The Hankel Determinants from a Singularly Perturbed Jacobi Weight

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2978
Author(s):  
Pengju Han ◽  
Yang Chen
Keyword(s):  
Logarithmic Derivative ◽  
Singularly Perturbed ◽  
Hankel Determinant ◽  
Compatibility Conditions ◽  
Operator Approach ◽  
Recurrence Coefficients ◽  
Ladder Operator ◽  
Jacobi Weight ◽  
Large N ◽  
Variable Substitution

We study the Hankel determinant generated by a singularly perturbed Jacobi weight w(x,s):=(1−x)α(1+x)βe−s1−x,x∈[−1,1],α>0,β>0s≥0. If s=0, it is reduced to the classical Jacobi weight. For s>0, the factor e−s1−x induces an infinitely strong zero at x=1. For the finite n case, we obtain four auxiliary quantities Rn(s), rn(s), R˜n(s), and r˜n(s) by using the ladder operator approach. We show that the recurrence coefficients are expressed in terms of the four auxiliary quantities with the aid of the compatibility conditions. Furthermore, we derive a shifted Jimbo–Miwa–Okamoto σ-function of a particular Painlevé V for the logarithmic derivative of the Hankel determinant Dn(s). By variable substitution and some complicated calculations, we show that the quantity Rn(s) satisfies the four Painlevé equations. For the large n case, we show that, under a double scaling, where n tends to ∞ and s tends to 0+, such that τ:=n2s is finite, the scaled Hankel determinant can be expressed by a particular PIII′.

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