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The optical soliton solutions of nonlinear Schrödinger equation with quintic non-Kerr nonlinear term
Results in Physics, 2023 The purpose of this paper is to study the optical soliton solutions of nonlinear Schrödinger equation with quintic non-Kerr nonlinear term describing the nonlinear wave state of optical solitons, which is a noteworthy and important model in optical fiber
Kun Zhang, Tianyong Han
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Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition [PDF]
, 2002 We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrodinger (NLS) equation, the $\lambda \
Ablowitz M +15 more
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Rogue waves on the double-periodic background in the focusing nonlinear Schrödinger equation. [PDF]
Physical Review E, 2019 The double-periodic solutions of the focusing nonlinear Schrödinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues.
Jinbing Chen +2 more
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Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation [PDF]
Inventiones Mathematicae, 2019 Consider the cubic nonlinear Schrödinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent.
T. Buckmaster +3 more
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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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Nonlinear Schrodinger equation and frequency saturation [PDF]
Analysis & PDE, 2011 We propose an approach that permits to avoid instability phenomena for the nonlinear Schrodinger equations. We show that by approximating the solution in a suitable way, relying on a frequency cut-off, global well-posedness is obtained in any Sobolev space with nonnegative regularity.
openaire +5 more sources
Journal of Applied Mathematics, 2012 We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable
Khaled A. Gepreel +2 more
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Probabilistic methods for discrete nonlinear Schr\"odinger equations [PDF]
, 2011 We show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation are exactly solvable in dimensions three and higher. A number of explicit formulas are derived.Comment: 30 pages, 2 figures. To appear in Comm.
Chatterjee, Sourav, Kirkpatrick, Kay
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Singular standing-ring solutions of nonlinear partial differential equations
, 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
Bricmont +30 more
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, 2005 In this paper we use a similarity transformation connecting some families of Nonlinear Schrodinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrodinger equation.
Abdullaev +28 more
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