[PDF] Top 20 Spline Solution for the Nonlinear Schrödinger Equation
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Spline Solution for the Nonlinear Schrödinger Equation
... This equation plays important roles in nonlinear ...many nonlinear phenomena including plasma physics [1], hydrodynamics [1] [2], self-focusing in laser pulses [3], propagation of heat pulses in ... See full document
11
The N soliton of the focusing nonlinear SchrÖdinger equation for N large
... We present a detailed analysis of the solution of the focusing nonlinear Schrö- dinger equation with initial condition ψ(x, 0 ) = N sech (x) in the limit N → ∞ . We begin by presenting new and more ... See full document
76
The Interaction and Degeneracy of Mixed Solutions for Derivative Nonlinear Schrödinger Equation
... and nonlinear optics. Firstly, the DNLS equation is used to describe the evolution of small but finite amplitude Alfvén waves that propagate quasi-parallel to the magnetic field [1] [2] and large-amplitude ... See full document
8
The global solution of anisotropic fourth order Schrödinger equation
... anisotropic nonlinear sixth order Schrödinger equation in ...the solution has been obtained and it scatters to a solution of the linearized equation as t → ∞ in ... See full document
17
Concentrating standing waves for the fractional Schrödinger equation with critical nonlinearities
... The goal of this paper is to show, by variational techniques as developed by Rabinowitz [], Wang [], Ding and Liu [] in the classical case, that semiclassical solutions con- centrate around some certain points that ... See full document
26
Riemann–Hilbert approach and N soliton solution for an eighth order nonlinear Schrödinger equation in an optical fiber
... with Equation (2) and convert it into a more convenient ...for Equation (2) is detailedly discussed in the framework of the Riemann–Hilbert problem without re- ... See full document
14
Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space
... martingale solution of problem ...stochastic nonlinear Schrödinger equations, notably [8,18,28], and references therein, in which the proofs of both the existence and the uniqueness were obtained by ... See full document
67
Derivation of the Nonlinear Schrödinger Equation by The Derivative Perturbation Expansion Method
... a nonlinear Schrödinger equation for modulations on a train of drift or Rossby waves in a very universal, if heuristic, ...The nonlinear Schr¨odinger equation has been widely studied in ... See full document
5
Schrödinger-type identity to the existence and uniqueness of a solution to the stationary Schrödinger equation
... the Schrödinger-type identity for obtaining transmutations via the fixed point index for nonlinear integral ...the Schrödinger-type identity method as basic blocks, among them are Fourier, sine and ... See full document
9
On the collapse of trial solutions for a damped driven nonlinear Schrödinger equation
... global solution is constructed by patching together solutions on finite intervals as constructed in the proof of Lemma ...global solution without patching, and we are going to show that the x-component of ... See full document
28
On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation
... nonlinear partial differential equations (in [7, 8, 15], the problem of the invariance is not considered). Second, at the time when “soliton” equations began to be inten- sively studied, there arose a question ... See full document
20
Conservative finite difference schemes for the chiral nonlinear Schrödinger equation
... In this paper, we derive three finite difference schemes for the chiral nonlinear Schrödinger equation (CNLS). The CNLS equation has two kinds of progressive wave solutions: bright and dark ... See full document
14
A mass conserved splitting method for the nonlinear Schrödinger equation
... From Figures 2, 3, and 4, we can obtain the conclusion that global existence of the solution is observed in the first two cases (cf. Figures 2, 3) and finite time blow-up is observed in the last case (cf. Figure ... See full document
13
Multiplicity of solutions of perturbed Schrödinger equation with electromagnetic fields and critical nonlinearity in RN
... By using the linking theorem twice to the corresponding functional, they established the existence results. Chabrowski and Szulkin [] considered problem (.) under assump- tion that V (x) changes sign; by using a ... See full document
14
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
Vector Nonlinear Schrödinger Equation on the half-line
... vector nonlinear Schrödinger equation (VNLS) on the ...one-dimensional nonlinear Schrödinger equation (NLS) along two directions: adding internal degrees of freedom and adding a ... See full document
24
Approximate Strongly Nonlinear Equation By Spline Method
... The advantage of SM can be concluded from Fig. 1 in which we compared the solution using SM with NM and HPM for particular values of the controlling parameters. Fig. 2 illustrates the velocity profile for ... See full document
7
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
Non polynomial spline method for the time fractional nonlinear Schrödinger equation
... In this paper, we have studied a numerical method based on cubic non-polynomial spline for the solution of a time-fractional nonlinear Schrödinger equation. By using the Fourier ... See full document
15
Stability Solution of the Nonlinear Schrödinger Equation
... .An important part of the local well-posed- ness theory is the study of how the strong solutions built in the past subsection depend upon the initial data. More accurate, we want to know if the small perturbation of ... See full document
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