# Questions tagged [non-linear-schroedinger]

The tag has no usage guidance.

27 questions
Filter by
Sorted by
Tagged with
39 views

### Derivation of non-linear Schrödinger equation from many-body QM

I hope this (and not MathOverflow) is the right place to post this question. I am a math student taking a methods of mathematical physics course, in which we cover the solution theory the non-linear ...
14 views

### Treatment of a light pulse moving from linear material A into non-linear material B

When I simulate the propagation of a pulse through a material without non-linear effects, I can use the non-linear schrödinger equation $$\partial_tE=\frac{i}{2k_0}\nabla^2E$$ with $k_0$ the wave ...
48 views

### Soliton solution of the NLS equation

My understanding of soliton - it is a moving pulse in a medium which does not change its structure with time. It has other properties like no interaction with other solitons (this could certainly be ...
92 views

### Lax pairs, Nonlinear Schrodinger Equation

Briefly: I have two Lax pairs in matrix form and using compatibility condition I have found a nonlinear partial differential equation system. I have searched this system very much seems the nonlinear ...
33 views

### Intuition behind focusing vs defocusing in integrable systems like NLS, KdV, mKdV

The following are examples of integrable systems arising from the AKNS system (check out AKNS paper here and a short Wikipedia description) Non-Linear Schrodinger equation Korteweg-de Vries equation ...
51 views

95 views

### Applications of optical rogue waves

It has been recently (2014) discovered that rogue waves arise not only in the context of deep sea waves, but also in that of fiber optics. To be precise, consider a single-mode fiber, which its slowly ...
654 views

### Aether existance in alternate universe made of Bose-Einstein condensate

I came across an interesting question which was shown to me by my professor, it is as follows: Investigation of an alternative Universe: This Universe contains three spatial and one time ...
247 views

54 views

While going through the derivation of Nonlinear Schrodingers equation from the Helmholtz equation I came across the following two pdes, $\nabla_\perp^2 F + \left[ \epsilon\left(\omega\right) k_0^2 - \... 0answers 33 views ### Solution to periodic potential GP equation Consider the boundary condition$\psi(0)=\psi(2\pi)$and the Hamiltonian (and corresponding nonlinear Schrödinger equation): $$\left[\left(-i\frac{\partial}{\partial\theta}-\Omega\right)^2+2\pi\gamma|\... 1answer 251 views ### How to define quantum chaos? I was told that quantum chaos is just a system whose Hamiltonian's classical version shows chaotic behavior. However, I just wondering what happens when one eigenstate of this Hamiltonian evolves? ... 0answers 87 views ### Nonlinear Saturated Schrodinger Equation in 1D- Physical Models I'm studying the Nonlinear 1d Schrodinger equation$$i\psi _t + \psi '' + |\psi |^{2p} \psi - \epsilon |\psi | ^{2q} \psi = 0\, , \quad t>0, x\in \mathbb{R}\, ,$$and specifically, its solitary ... 1answer 101 views ### Purpose of the multidimensional NLSE/GNLSE I know the purpose of the NLSE (Evolution of a complex field envelope in a nonlinear dispersive medium). Usually I am solving the 1d-GNLSE when simulating the propagation of a light pulse through a ... 0answers 180 views ### The Nonlinear Schrodinger Equation (NLSE) [closed] I am trying to show that the NLSE:$$\frac{\partial A(z,T)}{\partial z} = -i \frac{\beta_2}{2} \frac{\partial^2A}{\partial T^2} + i \gamma |A|^2 A$$may be cast in the form:$$\frac{\partial U(z,\... 0answers 90 views ### Nonlinear Schrodinger Equation perturbation stability Consider the nonlinear Schrödinger equation$i\frac{\partial A}{\partial z} -\frac{\beta_2}{2}\frac{\partial^2 A}{\partial T^2}+\gamma|A|^2A=0$This has steady state solution$A(z,T)=\sqrt{P_0}\exp\...
Consider the following nonlinear Schrödinger equation (NLSE): $$A_t+iA_{xx}+i|A|^2A = 0, \tag{1}$$ where $A$ is a complex valued function of $(x,t)$. A solution to this equation is A=a_oe^{-ia_o^2t}...
Suppose I want to solve a non-linear Schrödinger equation using imaginary time propagation to get the ground state solution. I choose $t = - i \tau$, and then solve the equation using the split-step ...