Nonlinear integral equations - Open Access .click

Applied Mathematics and Computation, 2005
Among various frequently used linear and nonlinear integral equations, which play important role in functional analysis, the authors consider the integral equation \[ \varphi(x,t)= f(x,t)+ \int^1_0 k(x,y) \gamma(y,\varphi(y, t))\,dy+ \int^t_0 F(t,\tau)\,\varphi(x,\tau)\,d\tau, \] where the notations are explained in the paper. Existence of the solution
M. A. Abdou 0001, Wagdy Gomaa El-Sayed, E. I. Deebs +2 more
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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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On the integrability of a nonlinear Schrödinger equation

Physica Scripta, 1994
Summary: It is shown that the nonlinear Schrödinger equation proposed by \textit{B. A. Malomed} and \textit{L. Stenflo} [J. Phys. A, Math. Gen. 24, No. 19, L1149--L1153 (1991; Zbl 0754.35161)] can be transformed to the cubic Schrödinger equation for a certain set of parameters and is thus integrable.
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Integral solution of a class of nonlinear integral equations

Applied Mathematics and Computation, 2013
This paper is concerned with the existence of integral solutions to a general nonlinear integral equationx(t)=f"1(t,x(@f"1(t)))+f"2t,@!"0^@f^"^2^(^t^)k(t,s)f"3(s,x(@f"3(s)))ds,t@?R^+.With the help of Krasnoselskii's fixed point theorem and the theory of measure of weak noncompactness, we establish a new and general existence theorem for the nonlinear ...
Jin Liang +3 more
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mathematics
other nonlinear integral equations
nls equations nonlinear schrödinger equations

fos: physical sciences
analysis
singular nonlinear integral equations

nonlinear volterra integral equation
monotonicity
nonlinear integral equation