Results 81 to 90 of about 32,605 (214)
An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity [PDF]
SIAM Journal on Numerical Analysis, 2003 This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrodinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant.
W. Bao, D. Jaksch
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Bright and Dark Breathers on an Elliptic Wave in the Defocusing mKdV Equation
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodically in the space‐time. For the defocusing modified Korteweg–de Vries equation, the construction of general breathers has been an open problem since the elliptic wave ...
Dmitry E. Pelinovsky, Rudi Weikard
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Advances in Difference Equations, 2021 Ablowitz–Kaup–Newell–Segur (AKNS) linear spectral problem gives birth to many important nonlinear mathematical physics equations including nonlocal ones.
Bo Xu, Yufeng Zhang, Sheng Zhang
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Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity [PDF]
, 2009 For a large class of nonlinear Schrodinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity, we prove the existence of nontrivial finite energy traveling waves moving with speed c in any space dimension N?3 ...
Mihai Marics
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Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.In this paper, we consider the initial value problem associated with the cubic nonlinear Schrödinger equation with third‐order dispersion ∂tu+iα∂x2u+β∂x3u+iγu2u=0,x∈ℝ,t∈ℝ,ux,0=u0x, where α, β and γ are real constants such that β, γ ≠ 0, u is a complex valued function and the initial data u0 is analytic on ℝ and has a uniform radius of analyticity σ0 in
Tegegne Getachew, Xiasheng Shi
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Rogue waves and periodic solutions of a nonlocal nonlinear Schrödinger model
Physical Review Research, 2020 In the present paper, a nonlocal nonlinear Schrödinger (NLS) model is studied by means of a recent technique that identifies solutions of partial differential equations by considering them as fixed points in space-time.
C. B. Ward +3 more
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.We investigate the Cauchy problem for the fourth‐order Schrödinger equation with quadratic nonlinearities involving second‐order derivatives: uxxu, uxxū, (ux)2, uūxx, and |ux|2, where u = u(x, t) is a complex‐valued function defined on R×R. The flow map of this Cauchy problem with the nonlinear terms uxxu or uxxū fails to be C2 differentiable at zero ...
Long Xiao, Ting Chen, Xian-Ming Gu
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Orbital stability of bound states of nonlinear Schrödinger equations with linear and nonlinear optical lattices [PDF]
, 2010 We study the orbital stability and instability of single-spike bound states of semi-classical nonlinear Schrödinger (NLS) equations with critical exponent, linear and nonlinear optical lattices (OLs).
Wei, Juncheng +5 more
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Long-time Instability and Unbounded Sobolev Orbits for Some Periodic Nonlinear Schrödinger Equations [PDF]
, 2012 We study the energy cascade problematic for some nonlinear Schrödinger equations on $${\mathbb{T}^2}$$T2 in terms of the growth of Sobolev norms. We define the notion of long-time strong instability and establish its connection to the existence of ...
Zaher Hani
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Journal of Mathematics, Volume 2026, Issue 1, 2026.In this work, we study the β‐fractional multicomponent Gross–Pitaevskii (G–P) system, which plays an important role in modeling Bose–Einstein condensates (BECs) and propagation in nonlinear waves. In Bose–Einstein condensation, the G–P equation is of great importance as it describes the condensate wave function’s behavior.
Naila Nasreen +5 more
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