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Integrable solutions of a functional-integral equation.
Revista Matemática Complutense, 1989 Under certain assumptions on the functions f,g,k the authors prove that the functional-integral equation \[ x(t)=g(t)+f(t,\int^{1}_{0}k(t,s)x(\phi (s))ds), \] \(t\in [0,1)\) has at least one solution \(x\in L^ 1[0,1]\), which is a.e. nonincreasing on \(L^ 1[0,1]\).
Z. Knap, J. Banaś
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Journal of Functional Analysis, 2008 We explore the connection between square-integrable solutions for real-values of the spectral parameter λ and the continuous spectrum of self-adjoint ordinary differential operators with arbitrary deficiency index d. We show that if, for all λ in an open
Aiping Wang, Jiong Sun, Anton Zettl
exaly +2 more sources
Integrable Kuralay Equations: Geometry, Solutions and Generalizations [PDF]
Symmetry, 2022 In this paper, we study the Kuralay equations, namely the Kuralay-I equation (K-IE) and the Kuralay-II equation (K-IIE). The integrable motion of space curves induced by these equations is investigated.
Zh.M. Sagidullayeva +3 more
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Overview of the Kadomtsev–Petviashvili-hierarchy reduction method for solitons
Partial Differential Equations in Applied Mathematics, 2022 The Kadomtsev–Petviashvili (KP) hierarchy reduction method is a prominent direct method for deriving explicit solutions to integrable equations. This method is based on Hirota’s bilinear formulation of integrable systems, as well as the observation that ...
Bo Yang, Jianke Yang
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Solutions to Integrable Space-Time Shifted Nonlocal Equations [PDF]
Reports on mathematical physics, 2021 In this paper we present a reduction technique based on bilinearization and double Wronskians (or double Casoratians) to obtain explicit multi-soliton solutions for the integrable space-time shifted nonlocal equations introduced very recently by Ablowitz
Shimin Liu, Jing Wang, Da‐jun Zhang
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Mathematics, 2022 In this paper, we deal with the existence of integrable solutions of Gripenberg-type equations with m-product of fractional operators on a half-line R+=[0,∞).
Ateq Alsaadi, M. Cichoń, M. Metwali
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Mathematics, 2021 In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient
A. El-Sayed, H. Hashem, S. Al-Issa
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On classical symmetries of ordinary differential equations related to stationary integrable partial differential equations [PDF]
Opuscula Mathematica, 2021 We study the relationship between the solutions of stationary integrable partial and ordinary differential equations and coefficients of the second-order ordinary differential equations invariant with respect to one-parameter Lie group.
Ivan Tsyfra
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Partial Differential Equations in Applied Mathematics, 2022 The complex coupled integrable dispersionless (CID)system is an important system. It has been shown that complex CID equation is gauge equivalent to the Pohlmeyer–Lund–Regge model (a complex sine-Gordon equation) and can also be transformed to the ...
Caiqin Song, Chen-Chen Fu, Zuo-Nong Zhu
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Integrated solution engineering [PDF]
Companion to the 21st ACM SIGPLAN symposium on Object-oriented programming systems, languages, and applications, 2006 Integrated Solution Engineering helps developers manage software complexity by offering semi-automated support for capturing and mining relationships among artifacts and/or developer tasks at different stages of the software lifecycle, and by aiding developers in the use and management of the information contained in these relationships.
Leiguang Gong +7 more
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