Browsing Bergen Open Research Archive by Author "Eychenne, Arnaud"
Now showing items 1-4 of 4
-
Asymptotic N -soliton-like solutions of the fractional Korteweg–de Vries equation
Eychenne, Arnaud (Journal article; Peer reviewed, 2023)We construct N-soliton solutions for the fractional Korteweg–de Vries (fKdV) equation ∂tu−∂x(∣D∣αu−u2)=0, in the whole sub-critical range α∈(1/2,2). More precisely, if Qc denotes the ground state solution associated ... -
Decay of solitary waves of fractional Korteweg-de Vries type equations
Eychenne, Arnaud; Valet, Frederic Fernand Jacques (Journal article; Peer reviewed, 2023)We study the solitary waves of fractional Korteweg-de Vries type equations, that are related to the 1- dimensional semi-linear fractional equations: |D|αu + u − f (u) = 0, with α ∈ (0, 2), a prescribed coefficient p∗(α), ... -
Strongly interacting solitary waves for the fractional modified Korteweg-de Vries equation
Eychenne, Arnaud; Valet, Frederic Fernand Jacques (Journal article; Peer reviewed, 2023)We study one particular asymptotic behaviour of a solution of the fractional modified Korteweg-de Vries equation (also known as the dispersion generalised modified Benjamin-Ono equation): ∂tu + ∂x(−|D|αu + u3) = 0. The ... -
A study of different interactions between solitary waves for fractional Korteweg-de Vries type equations
Eychenne, Arnaud (Doctoral thesis, 2023-01-13)Denne avhandlingen er satt sammen av tre artikler. I den første konstruerer vi $N$-soliton løsninger for den fractional Korteweg-de Vries (fKdV) ligningen $\partial_t u - \partial_x\left(|D|^{\alpha}u - u^2 \right)=0,$ i ...