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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 ...
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165 views

Deducing instability growth rates from the Hamiltonian for the nonlinear schrodinger equation

Consider the following nonlinear Schrodinger equation (NLSE): $$A_t+iA_{xx}+i|A|^2A = 0$$ where $A$ is a complex valued function of $(x,t)$. A solution to this equation is $A=a_oe^{-ia_o^2t}$. We ...
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340 views

Nonlinear waves and shock formation

In the cases of nonlinear acoustics, why is shock formation unlikely when the dispersion is strong when compared to the nonlinearity of the wave?
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814 views

Diifference between real time propagation and imaginary time propagation?

Suppose I want to solve Nonlinear Schrodinger equation using imaginary time propagation to get the ground state solution. I choose $t = - i t$, and then solve the equation using split step Crank ...