Results 81 to 90 of about 34,063 (197)
Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
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On the numerical evaluation of algebro-geometric solutions to integrable equations
, 2011 Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces.
Belokolos E +18 more
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Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities. [PDF]
Physical review. E, Statistical, nonlinear, and soft matter physics, 2009 It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients ...
Zhenya Yan, Zhenya Yan, V. Konotop
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On Standing Waves of 1D Nonlinear Schrödinger Equation With Triple Power Nonlinearity
Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.ABSTRACT For the one‐dimensional nonlinear Schrödinger equation with triple power nonlinearity and general exponents, we study analytically and numerically the existence and stability of standing waves. Special attention is paid to the curves of nonexistence and curves of stability change on the parameter planes.
Theo Morrison, Tai‐Peng Tsai
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Journal of Ocean Engineering and Science, 2020 In this paper, the variable coefficient nonlinear Schrödinger equation with fifth order dispersion in the inhomogeneous optical fiber is investigated to study the impact of fifth order dispersion on attosecond soliton propagation.
Angelin Vithya, M.S. Mani Rajan
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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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Stochastic Multisymplectic PDEs and Their Structure‐Preserving Numerical Methods
Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.ABSTRACT We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in Hydon [Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2005): 1627–1637].
Ruiao Hu, Linyu Peng
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Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics
Journal of Advanced Research, 2019 In nonlinear optics, the soliton transmission in different forms can be described with the use of nonlinear Schrödinger (NLS) equations. Here, the soliton transmission is investigated by solving the NLS equation with the reciprocal of the group velocity ...
Weitian Yu +4 more
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New Integrable Multi-Component NLS Type Equations on Symmetric Spaces: Z_4 and Z_6 Reductions [PDF]
, 2006 The reductions of the multi-component nonlinear Schrodinger (MNLS) type models related to C.I and D.III type symmetric spaces are studied. We pay special attention to the MNLS related to the sp(4), so(10) and so(12) Lie algebras. The MNLS related to sp(4)
Atanasov, V. A. +3 more
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Relaxation of solitons in nonlinear Schrödinger equations with potential [PDF]
, 2006 In this paper we study dynamics of solitons in the generalized nonlinear Schrodinger equation (NLS) with an external potential in all dimensions except for 2. For a certain class of nonlinearities such an equation has solutions which are periodic in time
Z. Gang, I. Sigal
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