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A maximisation technique for solitary waves: the case of the nonlocally dispersive Whitham equation
Mathias Nikolai Arnesen, Mats Ehrnstrom, Atanas G. Stefanov
Recently, two different proofs for large and intermediate-size solitary waves of the nonlocally dispersive Whitham equation have been presented, using either global bifurcation the…
Decay of solitary waves
Mathias Nikolai Arnesen
In this paper we consider the decay rate of solitary-wave solutions to some classes of non-linear and non-local dispersive equations, including for example the Whitham equation and…
A non-local approach to waves of maximal height for the Degasperis-Procesi equation
Mathias Nikolai Arnesen
We consider the non-local formulation of the Degasperis-Procesi equation , where is the non-local Fourier multiplier operator with symbol $m(ξ)=…
Non-uniform dependence on initial data for the Whitham equation
Mathias Nikolai Arnesen
We consider the Cauchy problem \begin{align*} \partial_t u+u\partial_x u+L(\partial_x u) &=0, \\ u(0,x)=u_0(x) \end{align*} on the torus and on the real line for a class of Fourier…
Existence of solitary-wave solutions to nonlocal equations
Mathias Nikolai Arnesen
We prove existence and conditional energetic stability of solitary-wave solutions for the two classes of pseudodifferential equations $ u_t+\left(f(u)\right)_x-\left(L u\right)_x=0…