Solitary waves for weakly dispersive equations with inhomogeneous nonlinearities

2019/02/14 by Maehlen, Ola
#35A01 (primary) #35A15 #35Q53 #76B03 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.05372

Abstract

We show existence of solitary-wave solutions to the equation u_t+ (Lu - n(u))_x = 0 , for weak assumptions on the dispersion L and the nonlinearity n. The symbol m of the Fourier multiplier L is allowed to be of low positive order (s > 0), while n need only be locally Lipschitz and asymptotically homogeneous at zero. We shall discover such solutions in Sobolev spaces contained in H^1+s.

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