Abstract
The focus of the present work is the one-dimensional nonlinear equation ut − uxxt + ux + uxxx + αuux = λ(uuxxx + 2uxuxx), (1) modeling the wave breaking phenomenon in the shallow water regime. When α, λ > 0, using a variational approximation, we show that (1) admits solitary wave solutions which propagate in the negative x−direction. AMS Subject Classification: 35Q35, 35Q51, 35A15
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