Modified wave operators for nonlinear Schrödinger equations in one and two dimensions.
Modified wave operators for the derivative nonlinear Schrödinger equation.
Modifying Lax Equations and the Second Hamiltonian Structure.
Modulation of the Camassa-Holm equation and reciprocal transformations
We derive the modulation equations (Whitham equations) for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit a bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry...
Modulation space estimates for Schrödinger type equations with time-dependent potentials
We give a new representation of solutions to a class of time-dependent Schrödinger type equations via the short-time Fourier transform and the method of characteristics. Moreover, we also establish some novel estimates for oscillatory integrals which are associated with the fractional power of negative Laplacian with . Consequently the classical Hamiltonian corresponding to the previous Schrödinger type equations is studied. As applications, a series of new boundedness results for the corresponding...
Modulational instability stabilization via complex Whitham deformations: Nonlinear Schrödinger equation
Moments and Huygens' principle for conformally invariant field equations in curved space-times
Monotone mappings and flows of viscous media.
Monotone solutions of a nonautonomous differential equation for a sedimenting sphere.
Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion
We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never...
Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions
We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability...
Moving domain walls in magnetic nanowires
Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors
In this paper we describe a non-local moving frame along a curve of pure spinors in , and its associated basis of differential invariants. We show that the space of differential invariants of Schwarzian-type define a Poisson submanifold of the spinor Geometric Poisson brackets. The resulting restriction is given by a decoupled system of KdV Poisson structures. We define a generalization of the Schwarzian-KdV evolution for pure spinor curves and we prove that it induces a decoupled system of KdV...
Multi solitary waves for nonlinear Schrödinger equations
Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations
We consider a mesoscopic model for phase transitions in a periodic medium and we construct multibump solutions. The rational perturbative case is dealt with by explicit asymptotics.
Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations
We consider a mesoscopic model for phase transitions in a periodic medium and we construct multibump solutions. The rational perturbative case is dealt with by explicit asymptotics.
Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields
In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer m, there exists ε(m) > 0 such that, for 0 < ε < ε(m), the problem has an m-bump complex-valued solution. As a result, when ε → 0, the equation has more and more multi-bump complex-valued solutions.
Multicomponent Burgers and KP hierarchies, and solutions from a matrix linear system.
Multicomponent models in nuclear astrophysics
We consider hydrodynamical models describing the evolution of a gaseous star in which the presence of thermonuclear reactions between several species leads to a multicomponent formulation. In the case of binary mixtures, recent 3D results are evoked. In the one-dimensional situation, we can prove global estimates and stabilization for some simplified model.
Multi-component NLS models on symmetric spaces: spectral properties versus representations theory.