In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large are large nonlinear exponents . In a second part, we compute...
In this paper, we present numerical methods
for the determination of solitons, that consist in spatially localized
stationary states of nonlinear scalar equations or coupled systems
arising in nonlinear optics.
We first use the well-known shooting method in order to find
excited states (characterized by the number of nodes) for the
classical nonlinear Schrödinger equation. Asymptotics can then
be derived in the limits of either large are large nonlinear
exponents .
In a second part, we compute...
We describe several results obtained recently on stochastic nonlinear Schrödinger equations. We show that under suitable smoothness assumptions on the noise, the nonlinear Schrödinger perturbed by an additive or multiplicative noise is well posed under similar assumptions on the nonlinear term as in the deterministic theory. Then, we restrict our attention to the case of a focusing nonlinearity with critical or supercritical exponent. If the noise is additive, smooth in space and non degenerate,...
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