Question

Sine integral as a soliton profile?

Answer 1

Among the most commonly known 1+1 soliton/solitary-wave profiles are:

tan−1(exp(x−vt))tan−1⁡(exp⁡(x−vt)) for Sine-Gordon,

tanh(x−vt)tanh⁡(x−vt) for ϕ4ϕ4,

sech2(x−vt)sech2⁡(x−vt) for KdV.

My question is:

Is there any known model in which the soliton profile takes the form of Sine Integral Si(x−vt)Si⁡(x−vt)?

EDIT:

More generally and correctly speaking, is there any soliton profile that wiggles similarly as the SiSi function? Especially topological solitons like Sine-Gordon or ϕ4ϕ4.

Answer 2

profile of the wave at time t to be the graph of the function x ↦→ u(x, t). .... such functions we can rewrite the integral as ..... NLS, and Sine- Gordon equation are also CPT-invariant.