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 …

Proving local well-posedness for quasi-linear problems in partial differential equations
presents a number of difficulties, some of which are universal and others of which are more …

In this article we prove short time local well-posedness in low-regularity Sobolev spaces for
large data general quasilinear Schrödinger equations with a nontrap** assumption …

We provide a unified viewpoint on two illposedness mechanisms for dispersive equations in
one spatial dimension, namely degenerate dispersion and (the failure of) the Takeuchi …

We present a novel method for establishing large data local well-posedness in low regularity
Sobolev spaces for general quasilinear Schrödinger equations with non-degenerate and …

We analyze the ground state of a Bose–Einstein condensate in the presence of higher-order
interaction (HOI), modeled by a modified Gross–Pitaevskii equation (MGPE). In fact, due to …

We consider a quasilinear KdV equation that admits compactly supported traveling wave
solutions (compactons). This model is one of the most straightforward instances of …

The skew mean curvature flow is an evolution equation for d dimensional manifolds
embedded in R d+ 2 (or more generally, in a Riemannian manifold). It can be viewed as a …

We prove a local in time well-posedness result for quasi-linear Hamiltonian Schrödinger
equations on T d for any d≥ 1. For any initial condition in the Sobolev space H s, with s …

The skew mean curvature flow is an evolution equation for a dimensional manifold
immersed into, and which moves along the binormal direction with a speed proportional to …