Results 21 to 30 of about 1,722 (89)
MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS
Forum of Mathematics, Pi, 2015 We consider the cubic nonlinear Schrödinger equation posed on the spatial domain $\mathbb{R}\times \mathbb{T}^{d}$. We prove modified scattering and construct modified wave operators for small initial and final data respectively ($1\leqslant d\leqslant 4$
ZAHER HANI +3 more
doaj +1 more source
On Classification of Integrable Davey-Stewartson Type Equations [PDF]
, 2013 This paper is devoted to the classification of integrable Davey-Stewartson type equations. A list of potentially deformable dispersionless systems is obtained through the requirement that such systems must be generated by a polynomial dispersionless Lax ...
Huard, Benoit, Novikov, Vladimir
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On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 7, Page 375-394, 2001., 2001 We consider the Cauchy problem periodic in the spatial variable for the usual cubic nonlinear Schrödinger equation and construct an infinite sequence of invariant measures associated with higher conservation laws for dynamical systems generated by this problem on appropriate phase spaces.
Peter E. Zhidkov
wiley +1 more source
Stability of solitary-wave solutions of coupled NLS equations with power-type nonlinearities
Advances in Nonlinear Analysis, 2015 This paper proves existence and stability of solitary-wave solutions of a system of 2-coupled nonlinear Schrödinger equations with power-type nonlinearities arising in several models of modern physics. The existence of vector solitary-wave solutions (i.e.
Bhattarai Santosh
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On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions
Abstract and Applied Analysis, Volume 6, Issue 6, Page 329-338, 2001., 2001 For stationary Schrödinger equation in ℝ n with the finite potential the singular pseudopotential is constructed in the form allowing us to find wave functions. The method does not require the knowledge of the explicit form of a potential and assumes only knowledge of the scattering amplitude for fixed level of energy.
Yuriy Valentinovich Zasorin
wiley +1 more source
Attractors of semigroups associated with nonlinear systems for diffusive phase separation
Abstract and Applied Analysis, Volume 1, Issue 2, Page 169-192, 1996., 1996 We consider a model for diffusive phase transitions, for instance, the component separation in a binary mixture. Our model is described by two functions, the absolutete temperature θ : = θ(t, x) and the order parameter w : = w(t, x), which are governed by a system of two nonlinear parabolic PDEs.
Nobuyuki Kenmochi
wiley +1 more source
On the derivation of the wave kinetic equation for NLS
Forum of Mathematics, Pi, 2021 A fundamental question in wave turbulence theory is to understand how the wave kinetic equation describes the long-time dynamics of its associated nonlinear dispersive equation.
Yu Deng, Zaher Hani
doaj +1 more source
Relativistic DNLS and Kaup-Newell Hierarchy [PDF]
, 2017 By the recursion operator of the Kaup-Newell hierarchy we construct the relativistic derivative NLS (RDNLS) equation and the corresponding Lax pair.
Lee, Jyh-Hao, Pashaev, Oktay K.
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On the instability for the cubic nonlinear Schrodinger equation
, 2007 We study the flow map associated to the cubic Schrodinger equation in space dimension at least three.
Burq +5 more
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Blow-up for self-interacting fractional Ginzburg-Landau equation
, 2017 The blow-up of solutions for the Cauchy problem of fractional Ginzburg-Landau equation with non-positive nonlinearity is shown by an ODE argument. Moreover, in one dimensional case, the optimal lifespan estimate for size of initial data is obtained ...
Fujiwara, Kazumasa +2 more
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