Question

if y=√ cos x² +√ cos x² + √cos x² + .....to ∞ then dy/dx is equal to
(1) -sin x/(2y-1)
(2) -2x sin x²/(2y-1)
(3) -sin²x/x(2y-1)
(4) none of these
with solutions please

Answer 1

Threshold solutions for the focusing 3d cubic Schroedinger equation

Jun 10, 2008 - arXiv:0806.1752v1 [math.AP] 10 Jun 2008. THRESHOLD SOLUTIONS FOR THE FOCUSING 3D CUBIC. SCHR¨ODINGER EQUATION. THOMAS DUYCKAERTS AND SVETLANA ROUDENKO. Abstract. ..... T.D. was partially supported by the French ANR Grant ONDNONLIN. Pa



The N-soliton of the focusing nonlinear Schroedinger equation for N

Aug 1, 2005 - Abstract. We present a detailed analysis of the solution of the focusing nonlinear Schrödinger equation ... an analysis of an ostensibly similar Riemann-Hilbert problem in the conditions of which a certain formal continuum limit .... M



The Nonlinear Schroedinger equation: solitons dynamics

Dec 22, 2008 - 35Q55, 35Q51, 37K40, 37K45,. 47J35. Keywords. Soliton dynamics, Nonlinear Schroedinger Equation, or- bital stability, concentration phenomena, semiclassical limit. Contents. 1 Introduction. 2. 1.1 Notations . . . . . . . . . . . . . .



Scattering for the non-radial 3D cubic nonlinear Schroedinger equation

Dec 4, 2007 - AP] 4 Dec 2007. SCATTERING FOR THE NON-RADIAL 3D CUBIC NONLINEAR. SCHR¨ODINGER EQUATION. THOMAS DUYCKAERTS, JUSTIN HOLMER, AND ... Scattering of radial H1 solutions to the 3D focusing cubic nonlinear .... T.D. was partially supported b



Scattering threshold for the focusing nonlinear Klein-Gordon equation

Jun 14, 2010 - Key words and phrases. nonlinear Klein-Gordon equation, scattering theory, blow-up solution, ground state, Sobolev .... Sattinger [39] proved on bounded domains the dichotomy into blow-up and global existence for solutions ...... We ca



Dam break problem for the focusing nonlinear Schr\" odinger equation

May 1, 2016 - with the dynamics of their formation and evolution, and with the statistics of their occurrence. In this paper we shall be concerned only with certain .... with the number of oscillatory phases g (the “genus� of the solution) at any



On universality of critical behaviour in the focusing nonlinear

Dec 3, 2007 - the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation. iϵΨt + ϵ2. 2 .... Our main goal is to find a replacement for the elliptic umbilic singularity when the disper- sive terms are added, i.e., we ... ha



Finite-well potential in the 3D nonlinear Schroedinger equation

Feb 12, 2007 - Using variational and numerical solutions we show that stationary negative-energy localized. (normalizable) bound ... 45.05.+x General theory of classical mechanics of discrete systems – 05.45.-a Nonlinear dynam- ...... H. Goldstein,



Nonlinear Schroedinger Equation in the Presence of Uniform

May 28, 2012 - ios. The most spectacular example of this approach was probably Einstein's use of his Principle of Equivalence in the development of General Relativity. Symmetries with important physical implications ... advanced in [5] (and the above



The Nonlinear Schroedinger Equation with a random potential

Aug 15, 2011 - in chaos and nonlinear physics. It may also stimulate novel experiments. On a one- dimensional lattice, the NLSE with a random potential (that will be ...... solution of the equation is assumed, it can be expanded in terms of the norma



A lattice model related to the nonlinear Schroedinger equation

Oct 2, 2009 - Rq = I ⊗ I − iRc,. Rc = κΠ λ − µ. (5). Here I is identical matrix 2X2 and Π is parmutation matrix. Lattice generalization of nS has long attracted attention of the experts [12, 13]. We propose a new version of lattice nS both



The focusing energy-critical nonlinear Schr\" odinger equation in

Apr 7, 2008 - then u is a global solution which does not blow up either forward or backward in time. Indeed, in this case .... for the solution u, x the spatial center function, and to C as the compactness modulus function. ...... future-spreading if



A Critical Centre-Stable Manifold for the Cubic Focusing Schroedinger

Aug 17, 2009 - by Coffman [Cof] for the cubic and Kwong [Kwo] and McLeod–Serrin [McSe] for more general nonlinearities. Equation (0.1) is invariant under Galilean coordinate transformations, ... However, in the course of the proof they are not allo



Soliton-like Solutions for Nonlinear Schroedinger Equation with

Nov 24, 2010 - linear part allows determination of the travelling wave argument z = βx + 2γy and the damping. (or amplifying) factor µ−1/2 of the soliton-like solution (2.3). Our balancing conditions (2.4) control dispersion, potential and nonli