[BOOK][B] Introduction to nonlinear dispersive equations
This textbook introduces the well-posedness theory for initial-value problems of nonlinear,
dispersive partial differential equations, with special focus on two key models, the Korteweg …
dispersive partial differential equations, with special focus on two key models, the Korteweg …
Benjamin-Ono and intermediate long wave equations: Modeling, IST and PDE
JC Saut - Nonlinear dispersive partial differential equations and …, 2019 - Springer
This survey article is focused on two asymptotic models for internal waves, the Benjamin-
Ono (BO) and Intermediate Long Wave (ILW) equations that are integrable by inverse …
Ono (BO) and Intermediate Long Wave (ILW) equations that are integrable by inverse …
Propagation of ultra-short optical pulses in cubic nonlinear media
T Schäfer, CE Wayne - Physica D: Nonlinear Phenomena, 2004 - Elsevier
We derive a partial differential equation that approximates solutions of Maxwell's equations
describing the propagation of ultra-short optical pulses in nonlinear media and which …
describing the propagation of ultra-short optical pulses in nonlinear media and which …
[BOOK][B] Harmonic analysis method for nonlinear evolution equations, I
1. Fourier multiplier, function space [symbol]. 1.1. Schwartz space, tempered distribution,
Fourier transform. 1.2. Fourier multiplier on L [symbol]. 1.3. Dyadic decomposition, Besov …
Fourier transform. 1.2. Fourier multiplier on L [symbol]. 1.3. Dyadic decomposition, Besov …
Ill-posedness issues for the Benjamin--Ono and related equations
L Molinet, JC Saut, N Tzvetkov - SIAM journal on mathematical analysis, 2001 - SIAM
We establish that the Cauchy problem for the Benjamin--Ono equation and for a rather
general class of nonlinear dispersive equations with dispersion slightly weaker than that of …
general class of nonlinear dispersive equations with dispersion slightly weaker than that of …
Ill-Posedness for a Class of Equations Arising in Hydrodynamics
We give a new approach to studying norm inflation (in some critical spaces) for a wide class
of equations arising in hydrodynamics. As an application, we prove strong ill-posedness of …
of equations arising in hydrodynamics. As an application, we prove strong ill-posedness of …
[PDF][PDF] Sharp well-posedness results for the BBM equation
JL Bona, N Tzvetkov - Discrete Contin. Dyn. Syst, 2009 - homepages.math.uic.edu
The regularized long-wave or BBM equation ut+ ux+ uux− uxxt= 0 was derived as a model
for the unidirectional propagation of long-crested, surface water waves. It arises in other …
for the unidirectional propagation of long-crested, surface water waves. It arises in other …
[PS][PS] An instability property of the nonlinear Schrödinger equation on S^d
We consider the NLS on spheres. We describe the nonlinear evolutions of the highest
weight spherical harmonics. As a consequence, in contrast with the at torus, we obtain that …
weight spherical harmonics. As a consequence, in contrast with the at torus, we obtain that …
[PDF][PDF] Global well-posedness of the KP-I initial-value problem in the energy space
arxiv:0705.4239v1 [math.AP] 29 May 2007 Page 1 arxiv:0705.4239v1 [math.AP] 29 May 2007
GLOBAL WELL-POSEDNESS OF THE KP-I INITIAL-VALUE PROBLEM IN THE ENERGY …
GLOBAL WELL-POSEDNESS OF THE KP-I INITIAL-VALUE PROBLEM IN THE ENERGY …
Well/Ill-posedness of the Boltzmann equation with soft potential
We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by
the methods from dispersive PDEs, we establish its sharp local well-posedness and ill …
the methods from dispersive PDEs, we establish its sharp local well-posedness and ill …