Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Long time asymptotics of the Camassa–Holm equation on the half-line
View through CrossRef
We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation
u
t
-
u
t
x
x
+
2
u
x
+
3
u
u
x
=
2
u
x
u
x
x
+
u
u
x
x
x
on the half-line
x
≥
0
. The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane
x
>
0
,
t
>
0
having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data associated with the initial and boundary values.
Title: Long time asymptotics of the Camassa–Holm equation on the half-line
Description:
We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation
u
t
-
u
t
x
x
+
2
u
x
+
3
u
u
x
=
2
u
x
u
x
x
+
u
u
x
x
x
on the half-line
x
≥
0
.
The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems.
We specify the regions in the quarter space-time plane
x
>
0
,
t
>
0
having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data associated with the initial and boundary values.
Related Results
Construction of new solutions to the fully nonlinear generalized Camassa-Holm equations by an indirect F function method
Construction of new solutions to the fully nonlinear generalized Camassa-Holm equations by an indirect F function method
An indirect F function method is introduced to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage...
Analyticity of the Cauchy Problem for a Three-Component Generalization of Camassa–Holm Equation
Analyticity of the Cauchy Problem for a Three-Component Generalization of Camassa–Holm Equation
In this paper, we investigate the Cauchy problem for a three-component generalization of Camassa–Holm equation (G3CH equation henceforth) with analytic initial data. The analyticit...
Long-range superharmonic Josephson current and spin-triplet pairing correlations in a junction with ferromagnetic bilayers
Long-range superharmonic Josephson current and spin-triplet pairing correlations in a junction with ferromagnetic bilayers
AbstractThe long-range spin-triplet supercurrent transport is an interesting phenomenon in the superconductor/ferromagnet ("Equation missing") heterostructure containing noncolline...
The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach
The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach
This work addresses the development of the Riemann-Hilbert problem (RHP) formalism (the Fokas method) for the Camassa-Holm equation under periodic boundary conditions. Particularly...
Turbulent Pressure Loss of Yield-fluids In Pipes
Turbulent Pressure Loss of Yield-fluids In Pipes
Abstract
A friction factor equation for yield fluids (yield-pseudoplastic, yield-dilatant, Bingham) was derived from flow equation under turbulent pipe flow condi...
The waveform comparison of three common-used fractional viscous acoustic wave equations
The waveform comparison of three common-used fractional viscous acoustic wave equations
Abstract
The forward simulation of the viscous acoustic wave equation is an essential part of geophysics and energy resources exploration research. The viscous acoustic sei...
Similarity Solutions for Shallow Hydraulic Fracture in Impermeable Rock
Similarity Solutions for Shallow Hydraulic Fracture in Impermeable Rock
ABSTRACT
The paper deals with the plane strain problem ofa shallow fluid-driven fracture propagating parallel to a free surface in an impermeable elastic rock. Fo...
Novel soliton dynamics via (G′∕G)-expansion neural networks approach in the modified Camassa–Holm and Kuramoto–Sivashinsky models
Novel soliton dynamics via (G′∕G)-expansion neural networks approach in the modified Camassa–Holm and Kuramoto–Sivashinsky models
This study investigates exact solitary wave solutions of the modified Camassa–Holm (mCH) and modified Kuramoto–Sivashinsky (mKS) equations, which are fundamental in fluid dynamics,...