On the soliton resolution and the asymptotic stability of N-soliton solution for the Wadati-Konno-Ichikawa equation with finite density initial data in space-time solitonic …
ZQ Li, SF Tian, JJ Yang - Advances in Mathematics, 2022 - Elsevier
In this work, we investigate the Cauchy problem of the Wadati-Konno-Ichikawa (WKI)
equation with finite density initial data in space-time solitonic regions, iq t+(q 1+| q| 2) xx= 0 …
equation with finite density initial data in space-time solitonic regions, iq t+(q 1+| q| 2) xx= 0 …
On the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regions
Y Yang, E Fan - Advances in Mathematics, 2022 - Elsevier
We study the long time asymptotic behavior for the Cauchy problem of the modified
Camassa-Holm (mCH) equation in the solitonic regions m t+(m (u 2− ux 2)) x+ κ ux= 0, m …
Camassa-Holm (mCH) equation in the solitonic regions m t+(m (u 2− ux 2)) x+ κ ux= 0, m …
[HTML][HTML] A view of the peakon world through the lens of approximation theory
H Lundmark, J Szmigielski - Physica D: Nonlinear Phenomena, 2022 - Elsevier
Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …
Soliton resolution for the Wadati–Konno–Ichikawa equation with weighted Sobolev initial data
ZQ Li, SF Tian, JJ Yang - Annales Henri Poincaré, 2022 - Springer
In this work, we employ the∂¯-steepest descent method to investigate the Cauchy problem
of the Wadati–Konno–Ichikawa (WKI) equation with initial conditions in weighted Sobolev …
of the Wadati–Konno–Ichikawa (WKI) equation with initial conditions in weighted Sobolev …
Long-time asymptotics for the Camassa–Holm equation
Long-time Asymptotics for the Camassa–Holm Equation Page 1 Copyright © by SIAM.
Unauthorized reproduction of this article is prohibited. SIAM J. MATH. ANAL. c 2009 Society for …
Unauthorized reproduction of this article is prohibited. SIAM J. MATH. ANAL. c 2009 Society for …
On the asymptotic stability of N-soliton solution for the short pulse equation with weighted Sobolev initial data
ZQ Li, SF Tian, JJ Yang - Journal of Differential Equations, 2023 - Elsevier
In this work, we are devoted to studying the Cauchy problem of the short pulse (SP) equation
with weighted Sobolev initial data. By developing the∂¯-generalization of Deift-Zhou …
with weighted Sobolev initial data. By developing the∂¯-generalization of Deift-Zhou …
A Riemann-Hilbert approach for the Degasperis-Procesi equation
AB de Monvel, D Shepelsky - arXiv preprint arXiv:1107.5995, 2011 - arxiv.org
We present an inverse scattering transform approach to the Cauchy problem on the line for
the Degasperis--Procesi equation $ u_t-u_ {txx}+ 3\omega u_x+ 4uu_x= 3u_xu_ {xx}+ uu …
the Degasperis--Procesi equation $ u_t-u_ {txx}+ 3\omega u_x+ 4uu_x= 3u_xu_ {xx}+ uu …
Inverse scattering transform for the coupled modified Korteweg-de Vries equation with nonzero boundary conditions
Y Xiao, E Fan, P Liu - Journal of Mathematical Analysis and Applications, 2021 - Elsevier
In this paper, we study the inverse scattering transform for the coupled modified Korteweg-
de Vries (cmKdV) equation with nonzero boundary conditions (NZBCs) at infinity. In order to …
de Vries (cmKdV) equation with nonzero boundary conditions (NZBCs) at infinity. In order to …
Soliton resolution for the short-pulse equation
Y Yang, E Fan - Journal of Differential Equations, 2021 - Elsevier
In this paper, we apply∂‾ steepest descent method to study the Cauchy problem for the
nonlinear short-pulse equation uxt= u+ 1 6 (u 3) xx, u (x, 0)= u 0 (x)∈ H (R), where H (R)= W …
nonlinear short-pulse equation uxt= u+ 1 6 (u 3) xx, u (x, 0)= u 0 (x)∈ H (R), where H (R)= W …
The short pulse equation by a Riemann–Hilbert approach
A Boutet de Monvel, D Shepelsky, L Zielinski - Letters in Mathematical …, 2017 - Springer
Abstract We develop a Riemann–Hilbert approach to the inverse scattering transform
method for the short pulse (SP) equation u_ xt= u+ 1 6 (u^ 3) _ xx uxt= u+ 1 6 (u 3) xx with …
method for the short pulse (SP) equation u_ xt= u+ 1 6 (u^ 3) _ xx uxt= u+ 1 6 (u 3) xx with …