The KP-II equation was derived by Kadmotsev and Petviashvili to explain stability of line solitary waves of shallow water. Recently, Mizumachi proved nonlinear stability of 1-line solitons for exponentially localized perturbations. In this paper, we prove stability of 1-line solitons for perturbations in (1 + x2)−1/2−0H1(ℝ2) and perturbations in H1(ℝ2) ∩ ∂xL2(ℝ2).

This article paper the influence of rails inclination on the behaviour of a railway vehicle in circulation on a curve and on alignment. A comparative study is performed the behaviour of a vehicle which circulates on rails without inclination and another circulating on inclined on rails. This study shows the interest on the inclined rails. The effects of the transverse and longitudinal stiffness of the primary suspension, the angle of inclination rail and the equivalent conicity of the wheels are considered to evaluate the vehicle's behaviour in curve and transverse stability. The simulation of the vehicle moving in curve with inclined rails shows that the transverse displacement of this vehicle decreases if the inclination of the rails increases. Moreover, the stability of a wheelset which circulates on inclined rails is comparable to the stability of a wheelset which circulates on the rail without inclination, and then the stability of the vehicle is preserved.