Generalized Jacobi elliptic function solution to a class of nonlinear Schrödinger-type equations.
Generalized kinetic equations and effective thermodynamics
We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can describe phase transitions and blow-up phenomena. On general grounds, our formalism can have applications in different domains of physics, astrophysics, hydrodynamics and biology. We find an aesthetic connexion between topics (stars, vortices, bacteries,...) which were...
Generalized solutions to the gKdV equation.
Generalized variational principle for long water-wave equation by He's semi-inverse method.
Generalized Weierstrass ...-functions and KP flows in affine spaces.
Generations of waves at an inertial surface due to explosions.
Generic properties of nonlinear boundary value problems
Generic solvability for the 3-D Navier-Stokes equations with nonregular force.
Geodesic equations on diffeomorphism groups.
Geodesic flow and two (super) component analog of the Camassa-Holm equation.
Geometric optics and instability for NLS and Davey-Stewartson models
We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrödinger equations with Gauge invariant power-law nonlinearities and nonlocal perturbations. The model includes the Davey-Stewartson system in its elliptic-elliptic and hyperbolic-elliptic variants. Our analysis reveals a new localization phenomenon for nonlocal perturbations in the high frequency regime and allows us to infer strong instability results on the Cauchy problem in negative order Sobolev...
Geometric realizations of bi-Hamiltonian completely integrable systems.
Geometric structure of magnetic walls
After a short introduction on micromagnetism, we will focus on a scalar micromagnetic model. The problem, which is hyperbolic, can be viewed as a problem of Hamilton-Jacobi, and, similarly to conservation laws, it admits a kinetic formulation. We will use both points of view, together with tools from geometric measure theory, to prove the rectifiability of the singular set of micromagnetic configurations.
Geometrical interpretation of the sinh-Gordon equation
Geometrical methods in hydrodynamics
We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.
Geometrische Eigenschaften der Lösungen der Differentialgleichung (1-zz)2wzz - n(n + 1) w= 0.
Geometry and analytic theory of Frobenius manifolds.
Geometry of fluid motion
We survey two problems illustrating geometric-topological and Hamiltonian methods in fluid mechanics: energy relaxation of a magnetic field and conservation laws for ideal fluid motion. More details and results, as well as a guide to the literature on these topics can be found in [3].
Geometry of KDV (1): Addition and the unimodular spectral classes.
This is the first of three papers on the geometry of KDV. It presents what purports to be a foliation of an extensive function space into which all known invariant manifolds of KDV fit naturally as special leaves. The two main themes are addition (each leaf has its private one) and unimodal spectral classes (each leaf has a spectral interpretation).
Geometry of KDV(4): Abel sums, Jacobi variety, and theta function in the scattering case.