Physics

Burgers' equation

Nonlinear system

Mathematics

Logarithm

Nonlinear Schrödinger equation

Gaussian

Mathematical analysis

Dispersion (optics)

Quantum mechanics

Traveling wave

Modern Physics Letters B

We present the complete analysis of traveling wave solutions to a special kind of nonlinear Schrödinger equation with logarithmic nonlinearity, and obtain all traveling wave solutions. As a result, we prove this equation does not have any Gaussian traveling wave solution. However, by modifying this equation into another form, we can actually obtain a Gaussian traveling wave solution, which verifies the conclusion that existing Gaussian traveling solution requires two restrictions: (1) balance between the dispersion terms and logarithmic nonlinearity; and (2) balance of the parameters.

On the Gaussian traveling wave solution to a special kind of Schrödinger equation with logarithmic nonlinearity