Results 231 to 240 of about 773 (267)

On asymptotic solutions of integrable wave equations

Physics Letters A, 2001
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Kamchatnov, A. M., Kraenkel, Roberto André, Umarov, B. A.   +2 more
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Asymptotic Solution to a Class of Nonlinear Volterra Integral Equations. II

SIAM Journal on Applied Mathematics, 1972
It is known that the nonlinear Volterra integral equation \[ \varphi (t)\pi ^{( - 1 / 2)} \,\int_0^t (t - s)^{{ - 1 / 2} } [ {f(s) - \varphi ^n (s)} ]ds,\quad t\geqq 0,\geqq n\geqq 1,\] has a continuous solution $\varphi (t) \geqq 0$ which is unique for each bounded and locally lntegrable function $f(t) \geqq 0$ Our prior investigation considered the ...
Olmstead, W. E., Handelsman, Richard A.
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Asymptotically Stable Solutions for a Nonlinear Functional Integral Equation

Acta Mathematica Vietnamica, 2015
The authors study the following integral equation \[ x(t)=V\left(t,x(t),\int_0^{\mu_1(t)}V_1\left(t,s,x\left(\sigma_1(s)\right),\int_0^{\mu_2(s)}V_2\left(t,s,r,x\left(\sigma_2(r)\right)\right)\, dr\right)\, ds\right) \] \[ +\int_0^{\infty}F\left(t,s,x\left(\chi_1(s)\right),\hdots,x\left(\chi_q(s)\right),\int_0^{\mu_3(s)}F_1\left(t,s,r,x\left(\sigma_3(r)
Ngoc, L. T. P., Long, N. T.
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On the Asymptotic Solution to a Class of Linear Integral Equations

SIAM Journal on Applied Mathematics, 1988
The author obtains complete uniform asymptotic expansions of the solutions to the integral equations \(Ku=f(x),\) and \(L_ xL^*_ XKu=f(x ...
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Asymptotic Solution of Palm's Integral Equation

Operations Research, 1963
The asymptotic solution of Palm's nonlinear integral equation is obtained, valid for channels sufficiently far away from the first channel. It is shown how the asymptotic formula may be applied, in certain cases, for the determination of the number of channels sufficient to serve a given Poisson input.
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Asymptotic analysis of the Marchenko integral equation and soliton asymptotics of a solution of the nonlinear schrödinger equation

Physica D: Nonlinear Phenomena, 1995
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Asymptotic Solutions of Some Nonlinear Volterra Integral Equations

SIAM Journal on Mathematical Analysis, 1981
The asymptotic behavior of solutions of three nonlinear Volterra integral equations of the form $u(t) + \int_0^t {A(t - s)g(u(s))ds = 0} $ is studied. These equations arise from certain diffusion problems, in dimensions 1, 2 or 3, with nonlinear boundary conditions.
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On the Oscillatory and Asymptotic Behavior of Solutions of Certain Integral Equations

Mediterranean Journal of Mathematics, 2016
The author studies the long time behavior of the solution of a 1D integral equation with fractional powers and non-locally vanishing and nonlinear weights. He shows that under some long time behavior of the weights, the solution is dominated by the source term, i.e., the term coming from the integral equation is indeed dominated by the source term. The
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Asymptotic Behavior of the Solution of the Integral Transport Equation in Slab Geometry

SIAM Journal on Applied Mathematics, 1977
We study the continuity and differentiability properties of the solution $\varphi $ of a linear integral equation arising in transport theory. The integral equation is described by an operator T which maps bounded functions into Holder continuous functions. T does not commute with the differential operator D.
Kaper, Hans G., Kellogg, R. Bruce
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On the asymptotic solution of a nonlinear Volterra integral equation

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1971
Abstract A technique based on the analytic continuation and study of the pole diagram of the Mellin transform has been described for obtaining asymptotic solution of nonlinear Volterra type integral equations for small and large values of the argument.
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