[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 …

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 …

[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 …

[HTML][HTML] New perturbed conformable Boussinesq-like equation: Soliton and other solutions

KS Nisar, L Akinyemi, M Inc, M Şenol, M Mirzazadeh… - Results in Physics, 2022 - Elsevier
In recent years, finding exact solutions to nonlinear differential equations has become a
fascinating study topic. In the present study, using the modified Kudryashov method and the …

On an integrable two-component Camassa–Holm shallow water system

A Constantin, RI Ivanov - Physics Letters A, 2008 - Elsevier
The interest in the Camassa–Holm equation inspired the search for various generalizations
of this equation with interesting properties and applications. In this Letter we deal with such …

Wave-breaking and peakons for a modified Camassa–Holm equation

G Gui, Y Liu, PJ Olver, C Qu - Communications in Mathematical Physics, 2013 - Springer
In this paper, we investigate the formation of singularities and the existence of peaked
traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The …

Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions

G Zhang, Z Yan - Physica D: Nonlinear Phenomena, 2020 - Elsevier
In this paper, we present a systematical inverse scattering transform for both focusing and
defocusing nonlocal (reverse-space–time) modified Korteweg–de Vries (mKdV) equations …

Soliton solutions of generalized time-fractional Boussinesq-like equation via three techniques

G Akram, S Arshed, M Sadaf - Chaos, Solitons & Fractals, 2023 - Elsevier
Extraction of exact solutions for nonlinear PDEs has become very popular in recent years.
The presented work deals with the investigation of time fractional perturbed Boussinesq-like …

Long-time asymptotics for the Camassa–Holm equation

AB De Monvel, A Kostenko, D Shepelsky… - SIAM journal on …, 2009 - SIAM
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 …

Direct and inverse scattering problems of the modified Sawada–Kotera equation: Riemann–Hilbert approach

DS Wang, X Zhu - Proceedings of the Royal Society A, 2022 - royalsocietypublishing.org
It is known that both the Sawada–Kotera equation and the Kaup–Kupershmidt equation are
related with the same modified equation by different Miura transformations. There is …