Results 21 to 30 of about 746,627 (265)
Advances in Mathematical Physics, 2014 We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation.
H. Chachou Samet +3 more
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Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations [PDF]
J. Math. Phys. 55, 032701 (2014), 2014 For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions $\cn(x,m)$ and $\dn(x,m)$ with modulus $m$, then it also admits solutions in terms of their sum as well as difference.
arxiv +1 more source
Large-Order Asymptotics for Multiple-Pole Solitons of the Focusing Nonlinear Schrödinger Equation [PDF]
Journal of nonlinear science, 2018 We analyze the large-n behavior of soliton solutions of the integrable focusing nonlinear Schrödinger equation with associated spectral data consisting of a single pair of conjugate poles of order 2n.
Deniz Bilman, R. Buckingham
semanticscholar +1 more source
Singular standing-ring solutions of nonlinear partial differential equations [PDF]
Physica D: Nonlinear Phenomena, Volume 239, pp 1968-1983, 2010, 2009 We present a general framework for constructing singular solutions of nonlinear evolution equations that become singular on a d-dimensional sphere, where d>1. The asymptotic profile and blowup rate of these solutions are the same as those of solutions of the corresponding one-dimensional equation that become singular at a point.
arxiv +1 more source
Frontiers in Physics, 2020 This study reviews the Peregrine solitons appearing under the framework of a class of nonlinear Schrödinger equations describing the diverse nonlinear systems.
T. Uthayakumar +2 more
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Results in Physics, 2023 This article studies the generalized nonlinear Schrödinger equation, which is used to simulate the propagation model of optical pulses in Non-Kerr medium.
Kun Zhang, Zhao Li
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Nonlinear gauge transformation for a class of Schroedinger equations containing complex nonlinearities [PDF]
Rep. Math. Phys. 46, 113 (2000), 2002 We consider a wide class of nonlinear canonical quantum systems described by a one-particle Schroedinger equation containing a complex nonlinearity. We introduce a nonlinear unitary transformation which permits us to linearize the continuity equation.
arxiv +1 more source
On recovering the nonlinearity for generalized higher-order Schrödinger equations [PDF]
, 2023 In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\"odinger equations to higher-order Schr\"odinger equations with a more general nonlinearity. More precisely, we consider a spatially-localized nonlinear higher-order Schr\"odinger equation and recover the spatially-localized coefficient by the ...
arxiv +1 more source
Results in Physics, 2021 The fractional (3+1)-dimensional nonlinear Schrödinger equation with cubic–quintic–septic nonlinearities plays a significant role in the study of ultra-short pulses in highly nonlinear optical phenomena.
Hira Tariq +6 more
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Applied Sciences, 2019 In this paper, the cubic-quartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation in parabolic law media are investigated to obtain the dark, singular, bright-singular combo and periodic soliton solutions. Two powerful methods, the m + G
Wei Gao +4 more
semanticscholar +1 more source