Modified wave operators for the derivative nonlinear Schrödinger equation.
Modifying Lax Equations and the Second Hamiltonian Structure.
Modular Forms of Varying Weight. I.
Modular forms of varying weights.
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 multilinear pseudodifferential operators
We prove that for symbols in the modulation spaces , p ≥ q, the associated multilinear pseudodifferential operators are bounded on products of appropriate modulation spaces. In particular, the symbols we study here are defined without any reference to smoothness, but rather in terms of their time-frequency behavior.
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
Module structure in Conley theory with some applications
A multiplicative structure in the cohomological version of Conley index is described following a joint paper by the author with K. Gęba and W. Uss. In the case of equivariant flows we apply a normalization procedure known from equivariant degree theory and we propose a new continuation invariant. The theory is applied then to obtain a mountain pass type theorem. Another illustrative application is a result on multiple bifurcations for some elliptic PDE.
Moltiplicatori spettrali per l'operatore di Ornstein-Uhlenbeck
Questa è una rassegna di alcuni risultati recenti sui moltiplicatori spettrali dell'operatore di Ornstein-Uhlenbeck, un laplaciano naturale sullo spazio euclideo munito della misura gaussiana. I risultati sono inquadrati nell'ambito della teoria generale dei moltiplicatori spettrali per laplaciani generalizzati.
Moments and Huygens' principle for conformally invariant field equations in curved space-times
Monge solutions for discontinuous hamiltonians
We consider an Hamilton-Jacobi equation of the formwhere is assumed Borel measurable and quasi-convex in . The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation (1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.
Monge solutions for discontinuous Hamiltonians
We consider an Hamilton-Jacobi equation of the form where H(x,p) is assumed Borel measurable and quasi-convex in p. The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation ([see full text]) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also...
Monge-Ampère equations and surfaces with negative Gaussian curvature
In [24], we studied the singularities of solutions of Monge-Ampère equations of hyperbolic type. Then we saw that the singularities of solutions do not coincide with the singularities of solution surfaces. In this note we first study the singularities of solution surfaces. Next, as the applications, we consider the singularities of surfaces with negative Gaussian curvature. Our problems are as follows: 1) What kinds of singularities may appear?, and 2) How can we extend the surfaces beyond the singularities?...
Monge-Ampère equationsviewed from contact geometry
Monogenic functions on surfaces.
Monoton konvergente Iterationsprozesse zur Lösung diskretisierter nichtlinearer Randwertprobleme
Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux
For scalar conservation laws in one space dimension with a flux function discontinuous in space, there exist infinitely many classes of solutions which are L1 contractive. Each class is characterized by a connection (A,B) which determines the interface entropy. For solutions corresponding to a connection (A,B), there exists convergent numerical schemes based on Godunov or Engquist−Osher schemes. The natural question is how to obtain schemes, corresponding to computationally less expensive monotone...
Monotone Explicit Iterations of the Finite Element Approximations for the Nonlinear Boundary Value Problem.
Monotone extensions of operators and the first boundary value problem