Results 121 to 130 of about 18,904 (165)

Nonlinear Integral Equations

2012
A nonlinear integral equation is an integral equation in which the unknown function appears in the equation in a nonlinear manner. The nonlinearity may occur either inside or outside of the integrand or simultaneously in both of these locations. It leads to an astonishing variety of new phenomena related to the characteristics of the solutions and to ...
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Tzitzéica Equation and Proliferation of Nonlinear Integrable Equations

Theoretical and Mathematical Physics, 2002
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Borisov, A. B., Zykov, S. A., Pavlov, M. V.   +2 more
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Engineering integrable nonautonomous nonlinear Schrödinger equations

Physical Review E, 2009
We investigate Painlevé integrability of a generalized nonautonomous one-dimensional nonlinear Schrödinger (NLS) equation with time- and space-dependent dispersion, nonlinearity, and external potentials. Through the Painlevé analysis some explicit requirements on the dispersion, nonlinearity, dissipation/gain, and the external potential as well as the ...
Xu-Gang, He, Dun, Zhao, Lin, Li, Hong-Gang, Luo   +3 more
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Nonlinear Singular Integral Equations

2011
Abel’s integral equation, linear or nonlinear, occurs in many branches of scientific fields [1], such as microscopy, seismology, radio astronomy, electron emission, atomic scattering, radar ranging, plasma diagnostics, X-ray radiography, and optical fiber evaluation. Linear Abel’s integral equation is the earliest example of an integral equation.
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VOLTERRA INTEGRAL EQUATIONS AND NONLINEAR SEMIGROUPS

Nonlinear Analysis: Theory, Methods & Applications, 1977
Publisher Summary This chapter discusses Volterra integral equations and nonlinear semigroups. It presents the nonlinear Volterra integral equation x ( t ) = y ( t ) + ∫ g ( t − s , x ( s )) ds , t ≥ 0, where H is a Hilbert space, y : [0, ∞) → H is given, g : [0, ∞) × H → satisfies a Lipschitz condition in its second place, and x :
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Nonlinear Fredholm Integral Equations

2011
It was stated in Chapter 4 that Fredholm integral equations arise in many scientific applications. It was also shown that Fredholm integral equations can be derived from boundary value problems. Erik Ivar Fredholm (1866–1927) is best remembered for his work on integral equations and spectral theory.
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Exact integration of nonlinear Schr�dinger equation

Theoretical and Mathematical Physics, 1988
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Its, A. R., Rybin, A. V., Sall', M. A.
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Nonlinear Volterra Integral Equations

2011
It is well known that linear and nonlinear Volterra integral equations arise in many scientific fields such as the population dynamics, spread of epidemics, and semi-conductor devices. Volterra started working on integral equations in 1884, but his serious study began in 1896. The name integral equation was given by du Bois-Reymond in 1888.
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Nonlinear Integral Equations

The Annals of Mathematics, 1955
Cameron, R. H., Shapiro, J. M.
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Integrable nonlinear equations on a half-axis

Ukrainian Mathematical Journal, 1991
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