[PDF] Top 20 The Mass Critical for the Nonlinear Schrödinger Equation in d = 2
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The Mass Critical for the Nonlinear Schrödinger Equation in d = 2
... Zhang, “Global Well-Posedness and Scattering for the Defocusing Mass-Critical Nonlinear Schrödinger Equation for Radial Data in High Dimensions,” Duke Mathematical Journal, Vol.. Zhang, [r] ... See full document
9
On the Stability of the Defocusing Mass Critical Nonlinear Schrödinger Equation
... u ≤ C M M L ′ . (14) The rest of the paper is organized as follows. In Section 2, we introduce our notations and state some previous results. In Section 3, we finally prove Theorem 2, except for proving a ... See full document
7
Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space
... We remark that in the special case of compact M, Burq, Gérard and Tzvetkov proved (B.4) even for ε = 0. But for our application in Sect. 7, this is not needed, such that we can prove uniqueness on non-compact manifolds ... See full document
67
Stability Solution of the Nonlinear Schrödinger Equation
... the mass critical, mass-supercritical and energy-subcritical of so- lution to the nonlinear Schrödinger ...the mass critical solu- tions and in section four ... See full document
8
Unconditional uniqueness results for the nonlinear Schrödinger equation
... R d )) to solve the corresponding integral equa- ...< d/2, typical choices for X are mixed Lebesgue spaces (Strichartz norms) [6] or Fourier restriction spaces ... See full document
29
Deriving the (0+2) Cubic Nonlinear Schrödinger Equation from the Theory of Subsonic Compressible Aerodynamics
... cubic nonlinear Schrödinger (NLS) equation within the convected wave equation for compressible ...NLS equation means that frictionless solitons and other nonlinear vortex ... See full document
17
Multiple solutions to nonlinear Schrödinger equations with critical growth
... In 2000, Cingolani and Lazzo (J. Differ. Equ. 160:118-138, 2000) studied nonlinear Schrödinger equations with competing potential functions and considered only the subcritical growth. They related the number ... See full document
20
Computational Methods for Three Coupled Nonlinear Schrödinger Equations
... obtained and novel shape changing in elastic collision property has been brought out. The system for N = 3 is of physical interest, in optical communication, and in bio- physics this system can be used to study the ... See full document
23
Concentrating standing waves for the fractional Schrödinger equation with critical nonlinearities
... The nonlinear self-coupling f (ψ ), which de- scribes a self-interaction in quantum electrodynamics, gives a closer description of many particles found in the real ...the nonlinear function f can be both a ... See full document
26
Non Scattering of the Solution of the Nonlinear Schrödinger Equation on the Torus
... DOI: 10.4236/jamp.2017.59162 1922 Journal of Applied Mathematics and Physics [5] Colliander, J., Keel, M., Staffilani, G., Takaoka, H. and Tao, T. (2010) Transfer of Energy to High Frequencies in the Cubic Defocusing ... See full document
6
The Interaction and Degeneracy of Mixed Solutions for Derivative Nonlinear Schrödinger Equation
... DOI: 10.4236/jamp.2019.711180 2651 Journal of Applied Mathematics and Physics soliton in a certain limiting condition. Determinant expression of the N-soliton solution [9] for the DNLS equation can be expressed by ... See full document
8
On the collapse of trial solutions for a damped driven nonlinear Schrödinger equation
... Furthermore, compared with α > 1/2, which is the consequence of condition β > 1/2, α ≥ β ≥ α/2 from case a > 0, the extra condition α > 1 is in a way counter intuitive for negative a. ... See full document
28
On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation
... the spatial variable for a one-dimensional NLS with the power nonlinearity κ|ψ| p−1 ψ, constructed a bounded IM for κ = − 1 and 1 < p < 5. Similar results are contained in [16, 25, 28] (with 1 < p < 3 if κ = ... See full document
20
Structure and dynamics of solitary waves in fluid media
... Gardner–Ostrovsky equation which is applicable only within a finite range of ...the nonlinear Schr€ odinger equation (NLSE) which describes the evolution of narrow-band wave-trains and show that ... See full document
135
Derivation of the Nonlinear Schrödinger Equation by The Derivative Perturbation Expansion Method
... IN the field of plasma physics, the zonal flow[1] refers to a mean poloidal flow with strong variation along the minor radius of the toroidal confinement. (shear property). This phenomenon is important in toroidal ... See full document
5
Infinitely many weak solutions for a fractional Schrödinger equation
... fractional Schrödinger equation (– ) α u + V(x)u = f (x,u), x ∈ R N , where 0 < α < 1, N > 2 α , (– ) α stands for the fractional Laplacian of order α , V is a positive continuous potential, ... See full document
14
Spline Solution for the Nonlinear Schrödinger Equation
... In the past few years a great deal of efforts has been expended to solve NLS equations. It is more difficult to find the analytical solutions of the NLS equation, so the study of the numerical solution of NLS ... See full document
11
The local well-posedness for nonlinear fourth-order Schrödinger equation with mass-critical nonlinearity and derivative
... where u(x, t) are complex-valued function, u(x, ¯ t) is the complex conjugate quantity of u(x, t). a, b, and c are real numbers. We are interested in obtaining the well-posedness for the Cauchy problem of (.) with ... See full document
11
The Pfaffian Technique: A (2 + 1) Dimensional Korteweg de Vries Equation
... It is known that many nonlinear evolution equations have soliton solutions, such as the Korteweg de Vries equation, the Sin-Gordon equation, the nonlinear Schrödinger equation, the Kadom[r] ... See full document
6
Scattering of the Radial Focusing Mass Supercritical and Energy Subcritical Nonlinear Schrödinger Equation in 3D
... The argument of [6] in the radial case followed a strategy introduced by [7] for proving global well-pos- edness and scattering for the focusing energy-critical NLS. The beginning used a contradiction to the ... See full document
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