Nonsymmetric solutions for some variational problems

Solitary waves for a class of generalized Kadomtsev-Petviashvili equation in RN with positive and zero mass

“…Recently Alves and Miyagaki [3] have treated the case non autonomous, getting results similar to those obtained in, for instance, [13,14], and also the regularity properties of the solutions. Paumond in [30] obtained nonsymmetric solutions for (1.1) with N = 5, extending those results in [13,14].…”

Asymptotics of the solitary waves for the generalized Kadomtsev-Petviashvili equations

“…We do not actually know of any non-trivial solitary waves which verify such assumption, but we believe that they may exist. Indeed, L. Paumond [13] proved their existence in dimension N = 5 for an equation very similar to equation (1), namely  …”

“…However, such spaces are not suitable to describe their singularities near the origin. Indeed, their singularities are anisotropic because of the anisotropy of their Fourier transforms given by formulae (12), (13) and (14).…”

“…The proofs of Theorems 3 and 4 rely on the form of the Fourier transforms of H 0 , K 0 and K k . By formulae (12), (13) and (14), they are rational fractions given by…”