Results 51 to 60 of about 18,904 (165)

Integrable nonlinear equations and Liouville's theorem, I [PDF]

Communications in Mathematical Physics, 1981
A symplectic structure is constructed and the Liouville integration carried out for a stationary Lax equation [L, P]=0, whereL is a scalar differential operator of an arbitrary order.nth order operators are included into the variety of first-order matrix operators, and properties of this inclusion are studied.
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Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

The Scientific World Journal, 2014
A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation.
S. Mashayekhi, M. Razzaghi, O. Tripak
doaj   +1 more source

DARBOUX-INTEGRABLE EQUATIONS WITH NON-ABELIAN NONLINEARITIES

Probing the Structure of Quantum Mechanics, 2002
We introduce a new class of nonlinear equations admitting a representation in terms of Darboux-covariant compatibility conditions. Their special cases are, in particular, (i) the "general" von Neumann equation $i\dot =[H,f( )]$, with $[f( ), ]=0$, (ii) its generalization involving certain functions $f( )$ which are non-Abelian in the sense that ...
Ustinov, N.v., Czachor, Marek
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Learning nonlinear integral operators via recurrent neural networks and its application in solving integro-differential equations

Machine Learning with Applications
In this paper, we propose using LSTM-RNNs (Long Short-Term Memory-Recurrent Neural Networks) to learn and represent nonlinear integral operators that appear in nonlinear integro-differential equations (IDEs).
Hardeep Bassi, Yuanran Zhu, Senwei Liang, Jia Yin, Cian C. Reeves, Vojtěch Vlček, Chao Yang   +6 more
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Strongly Nonlinear Integral Equations of Hammerstein Type [PDF]

Proceedings of the National Academy of Sciences, 1975
This paper studies the solution of the nonlinear Hammerstein equation u ( x ) + ʃ k ( x,y ) f [ y,u ( y )]μ( dy ) = h (
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Nonlinear Alternative: Application to an Integral Equation [PDF]

Journal of Applied Analysis, 1999
Using the nonlinear alternative for compact mappings it is shown that the nonlinear integral equation \[ u^2(t)=L(t)+\int^1_0K(t-s)u(s)ds(t\geq 0)\tag{1} \] has a nonnegative solution defined on \(\mathbb{R}_+\). The equation (1) is connected with modeling of infiltration of a fluid in an isotropic homogeneous porous medium.
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BVφ-solutions of nonlinear integral equations

Journal of Mathematical Analysis and Applications, 2003
Let \(\mathbb{R}_+= [0,+\infty)\) and let \(\Phi: \mathbb{R}_+\to \mathbb{R}_+\) be a continuous, unbounded, nondecreasing function such that \(\Phi(u)= 0\Leftrightarrow u= 0\). Assume that \(\Phi\) satisfies the condition \(\Delta_2\) for small \(u\) i.e.
Bugajewska, Daria, Bugajewski, Dariusz, Hudzik, Henryk   +2 more
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ALGEBRAIC NONLINEARITY IN VOLTERRA-HAMMERSTEIN EQUATIONS [PDF]

Journal of Sciences, Islamic Republic of Iran, 1999
Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and ...
doaj  

Existence Theorem for Integral and Functional Integral Equations with Discontinuous Kernels

Abstract and Applied Analysis, 2012
Existence of extremal solutions of nonlinear discontinuous integral equations of Volterra type is proved. This result is extended herein to functional Volterra integral equations (FVIEs) and to a system of discontinuous VIEs as well.
Ezzat R. Hassan
doaj   +1 more source

Implicit Integral Equations with Discontinuous Nonlinearities

Journal of Integral Equations and Applications, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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