5 problems

Whitham's conjecture. The equation should be capable of predicting both breaking and peaking of waves. Here, breaking means the evolutionary formation of bounded solutions with inf…

A highest cusped traveling wave for the Whitham equation is a periodic traveling-wave profile with crests at its singular points; its regularity is $C^{1/2}$. Ehrnström and Wahlén'…

Let the Whitham equation be considered with initial data $u_0$ of sufficiently large mass, and let $t_c$ denote the characteristic breaking time. A cusp at time $t^*>t_c$ has a spa…

Consider a solitary wave solution of the Whitham equation with surface tension parameter $\beta$. Transverse stability conjecture. The Whitham solitary wave should be transversally…

Let $u_0\in L_2(\mathbb{R})$ be smooth initial data with a single negative hump. For $-1<\alpha<0$, solutions to the Whitham equation and to the fKdV equations with sufficiently sm…