Questions tagged [non-linear-schroedinger]

10 questions with no upvoted or accepted answers
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Inverse Scattering Transform (IST) for the Linear Schrödinger Equation

I know that the Inverse Scattering Transform (IST) has been employed to solve, for instance, the KdV equation and I believe also other nonlinear PDEs, such as the NLS. However, if we consider the ...
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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 ...
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58 views

Is the Schrödinger-Newton equation time-reversal symmetric? What about PT-symmetry or similar symmetries?

I tried to figure it out myself. If you take the integro-differential form of the equation, a complex square of the time-dependent wavefunction appears.. It seems to me that this means the equation ...
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97 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 ...
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0answers
34 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 ...
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54 views

Mode distribution and Phase constant for nonlinear optical fiber

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 - \...
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0answers
35 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|\...
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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 ...
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91 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\...
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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 ...