[图书][B] Handbook of nonlinear partial differential equations: exact solutions, methods, and problems

AD Polyanin, VF Zaitsev - 2003 - taylorfrancis.com
The Handbook of Nonlinear Partial Differential Equations is the latest in a series of
acclaimed handbooks by these authors and presents exact solutions of more than 1600 …

Stability of peakons

A Constantin, WA Strauss - … : A Journal Issued by the Courant …, 2000 - Wiley Online Library
The peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation
that is a model in shallow water theory and the theory of hyperelastic rods. We give a very …

Existence of permanent and breaking waves for a shallow water equation: a geometric approach

A Constantin - Annales de l'institut Fourier, 2000 - numdam.org
Existence of permanent and breaking waves for a shallow water equation: a geometric
approach Page 1 ANNALES DE L’INSTITUT FOURIER ADRIAN CONSTANTIN Existence of …

The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations

A Constantin, D Lannes - Archive for Rational Mechanics and Analysis, 2009 - Springer
In recent years two nonlinear dispersive partial differential equations have attracted much
attention due to their integrable structure. We prove that both equations arise in the …

Soliton resolution for the complex short pulse equation with weighted Sobolev initial data in space-time solitonic regions

ZQ Li, SF Tian, JJ Yang, E Fan - Journal of Differential Equations, 2022 - Elsevier
In this work, we employ the∂¯-steepest descent method to investigate the Cauchy problem
of the complex short pulse (CSP) equation with initial conditions in weighted Sobolev space …

[图书][B] Nonlinear water waves with applications to wave-current interactions and tsunamis

A Constantin - 2011 - SIAM
This book is the written and somewhat expanded version of the author's lectures delivered at
the NSF-CBMS international research conference organized at the Mathematics Department …

Global conservative solutions of the Camassa–Holm equation

A Bressan, A Constantin - Archive for Rational Mechanics and Analysis, 2007 - Springer
This paper develops a new approach in the analysis of the Camassa–Holm equation. By
introducing a new set of independent and dependent variables, the equation is transformed …

Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation

YA Li, PJ Olver - Journal of Differential Equations, 2000 - Elsevier
We establish local well-posedness in the Sobolev space Hs with any s> 3 2 for an integrable
nonlinearly dispersive wave equation arising as a model for shallow water waves known as …

Camassa–Holm, Korteweg–de Vries and related models for water waves

RS Johnson - Journal of Fluid Mechanics, 2002 - cambridge.org
In this paper we first describe the current method for obtaining the Camassa–Holm equation
in the context of water waves; this requires a detour via the Green–Naghdi model equations …

A few remarks on the Camassa-Holm equation

R Danchin - 2001 - projecteuclid.org
In the present paper, we use some standard a priori estimates for linear transport equations
to prove the existence and uniqueness of solutions for the Camassa-Holm equation with …