Spectral analysis of a fourth-order nonselfadjoint operator with nonsmooth coefficients

2015 ◽  
Vol 56 (1) ◽  
pp. 138-154 ◽  
Author(s):  
D. M. Polyakov
Keyword(s):  
Spectral Analysis ◽  
Fourth Order ◽  
Nonselfadjoint Operator ◽  
Nonsmooth Coefficients

scholarly journals On Singular Dissipative Fourth-Order Differential Operator in Lim-4 Case

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Ekin Uğurlu ◽  
Elgiz Bairamov
Keyword(s):  
Spectral Analysis ◽  
Differential Operator ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Inverse Operator ◽  
Order Differential Operator ◽  
Associated Functions ◽  
Fourth Order Differential Operator

A singular dissipative fourth-order differential operator in lim-4 case is considered. To investigate the spectral analysis of this operator, it is passed to the inverse operator with the help of Everitt's method. Finally, using Lidskiĭ's theorem, it is proved that the system of all eigen- and associated functions of this operator (also the boundary value problem) is complete.

scholarly journals Dynamic Behaviors of Soliton Solutions for a Three-Coupled Lakshmanan-Porsezian-Daniel Model

2021 ◽  
Author(s):  
Beibei Hu ◽  
Ji Lin ◽  
Ling Zhang
Keyword(s):  
Spectral Analysis ◽  
Fourth Order ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Nonlinear Dynamical ◽  
Jump Matrix ◽  
Dynamical Behaviors ◽  
Helical Protein ◽  
Order Dispersion ◽  
Dispersion Term

Abstract In this paper, we use the Riemann-Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan-Porsezian-Daniel (LPD) model, which describe the dynamics of alpha helical protein with the interspine coupling at the fourth-order dispersion term. Through the spectral analysis of Lax pair, we construct the higher order matrix RH problem for the three-coupled LPD model, when the jump matrix of this particular RH problem is a 4×4 unit matrix, the exact N-soliton solutions of the three-coupled LPD model can be exhibited. As special examples, we also investigate the nonlinear dynamical behaviors of the single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an integrable generalized N-component LPD model with its linear spectral problem is discussed.

Spectral analysis of a fourth-order differential pencil on the whole real line

2012 ◽  
Vol 85 (1) ◽  
pp. 57-59
Author(s):  
S. S. Mirzoev ◽  
E. G. Orudzhev ◽  
A. R. Aliev
Keyword(s):  
Spectral Analysis ◽  
Fourth Order ◽  
Real Line
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