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On nonlinearity parameter in Nonlinear Schrodinger Equation (NLS)

While I am studying the wave propagation in fluids, the amplitude modulation seems to be governed by the NLS equation. In some of the journal papers the nonlinearity parameter, $N$ seems to be of high ...
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114 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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92 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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493 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 ...