2025MNRAS.542L..73V

Flat rotational velocity curve out to 1 Mpc has been recently observed applying deprojection formula to infer the gravitational potential around isolated galaxies from weak gravitational lensing. Here, we focus on the theoretical self-consistent non-linear density wave model as an explanation for observed data, as an alternative to Lambda cold dark matter and Modified Newtonian Dynamics. The physics of this model relays on the non-linear soliton solution established in plasma physics applied on the spiral galaxy dynamics resolving several issues including flat rotational curve with baryonic matter only. This novel model is tested by baryonic Tully-Fisher relation (BTFR); expression of the rotational velocity from non-linear model is used to fit observed data by weak gravitational lensing. Fitted parameter, surface mass density, is used to calculate mass of the galaxy and construct BTFR, which agrees with BTFR obtained by weak gravity lensing; slope parameter is ${\sim} 4$, while the intercept is slightly higher indicating higher mass of the baryonic matter in the galaxy.