Probabilistic representation for solutions to nonlinear Fokker-Planck equations [PDF]
arXiv, 2018 One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear stochastic differential equation. The case of a nonlinear Fokker-Planck equation with linear space dependent drift is also
arxiv
Soliton dynamics in optical fiber based on nonlinear Schrödinger equation. [PDF]
Heliyon, 2023 Abdillah Mardi H +4 more
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From macroscopic irreversibility to microscopic reversibility via a nonlinear schrödinger‐type field equation [PDF]
, 1987 Dieter Schuch, K. Chung
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Regularization for fractional integral. Application to nonlinear equations with singularities [PDF]
arXiv, 2003 We give the regularization for fractional integral by delta sequence and apply it to obtain existence-uniqueness theorems in Colombeau algebras for nonlinear equations with singularities: nonlinear system of integral equations with polar kernel and nonlinear parabolic equations (of ordinary type, with nonlinear conservative term and with Schr\"odinger ...
arxiv
Soliton solutions of fractional extended nonlinear Schrödinger equation arising in plasma physics and nonlinear optical fiber. [PDF]
Sci Rep, 2023 Ahmad J +5 more
europepmc +1 more source
Action-angle variables for a multicomponent nonlinear Schrödinger equation [PDF]
, 1985 P. P. Kulish
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Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2012 We study the existence of positive solutions for the nonlinear Schrödinger equation with the fractional Laplacian \begin{gather*}(-\Delta)^{\alpha}u+u=f(x,u)\text{~in~}\mathbb{R}^{N},\\u>0\text{~in~}\mathbb{R}^{N},\qquad\lim_{|x|\rightarrow\infty}u(x)=0.\
P. Felmer, A. Quaas, Jinggang Tan
semanticscholar +1 more source
Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term
Abstract and Applied Analysis, 2013 A nonlinear Schrödinger equation with a higher-order dispersive term describing the propagation of ultrashort femtosecond pulses in optical fibres is considered and is transformed into a second-order nonlinear ordinary differential equation.
Rui Cao
doaj +1 more source
A new high-order compact ADI finite difference scheme for solving 3D nonlinear Schrödinger equation
Advances in Difference Equations, 2018 In this paper, firstly, we solve the linear 3D Schrödinger equation using Douglas–Gunn alternating direction implicit (ADI) scheme and high-order compact (HOC) ADI scheme, which have the order O(τ2+h2) $O(\tau^{2}+h^{2})$ and O(τ2+h4) $O(\tau^{2}+h^{4})$,
Rena Eskar, Pengzhan Huang, Xinlong Feng
doaj +1 more source
Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation. [PDF]
Sci Rep, 2023 Fan C, Li L, Yu F.
europepmc +1 more source