The Sturm-Liouville Hierarchy of Evolution Equations
Advanced Nonlinear Studies, 2011 Abstract We introduce a hierarchy of evolution equations based on the Sturm-Liouville equation −(pφ′)′ + qφ = λyφ. Our hierarchy includes the Korteweg-de Vries (K-dV) and the Camassa-Holm (CH) hierarchy. We determine a class of solutions of the hierarchy which are of algebro-geometric type.
JOHNSON, RUSSELL ALLAN, L. Zampogni
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Bounds of Eigenvalues for Complex q-Sturm–Liouville Problem
MathematicsThe eigenvalues of complex q-Sturm–Liouville boundary value problems are the focus of this paper. The coefficients of the corresponding q-Sturm–Liouville equation provide the lower bounds on the real parts of all eigenvalues, and the real part of the ...
Xiaoxue Han
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Indefinite Hamiltonian systems whose Titchmarsh–Weyl coefficients have no finite generalized poles of non-positive type [PDF]
, 2013 The two-dimensional Hamiltonian system (*) y'(x)=zJH(x)y(x), x∈(a,b), where the Hamiltonian H takes non-negative 2x2-matrices as values, and $J:= \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$, has attracted a lot of interest over the past decades ...
Harald Woracek +3 more
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Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics [PDF]
, 2010 In this paper we present computer-assisted proofs of a number of results in theoretical fluid dynamics and in quantum mechanics. An algorithm based on interval arithmetic yields provably correct eigenvalue enclosures and exclosures for non-self-adjoint ...
Langer, M. +4 more
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Wave equation for Sturm-Liouville operator with singular potentials [PDF]
, 2022 The paper is denoted to the initial-boundary value problem for the wave equation with the Sturm-Liouville operator with irregular (distributive) potentials.
Yeskermessuly, Alibek +2 more
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Programmable Multifunctional Bistable Structures for Energy Transfer and Dissipation. [PDF]
Adv Sci (Weinh)Utilizing the energy conversion characteristics of asymmetric bistable beams, this study develops a programmable multifunctional system composed of multiple bistable beams for energy transfer and dissipation. The high energy density enables the system to demonstrate potential in transient scenarios such as target delivery and shock absorption ...
Na X +6 more
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Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2020 In this paper, we consider the discrete Sturm-Liouville operator generated by second order difference equation with non-selfadjoint operator coefficient.
Esra Kır Arpat, Gökhan Mutlu
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The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points [PDF]
Sahand Communications in Mathematical Analysis, 2019 In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated.
Seyfollah Mosazadeh
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On strong singular fractional version of the Sturm–Liouville equation
Boundary Value Problems, 2021 The Sturm–Liouville equation is among the significant differential equations having many applications, and a lot of researchers have studied it. Up to now, different versions of this equation have been reviewed, but one of its most attractive versions is
Mehdi Shabibi +3 more
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Continuations of Hermitian indefinite functions and corresponding canonical systems : an example [PDF]
, 2004 M. G. Krein established a close connection between the continuation problem of positive definite functions from a finite interval to the real axis and the inverse spectral problem for differential operators.
Langer, M. +5 more
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