We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illus...

Economic models are used for many purposes, including forecasting and simulation. Economic models are generally nonlinear. Even simple macroeconomic models, where all the stochastic equations in the system may be linear in logarithms, need to be completed by accounting identities that are linear in levels. As a consequence, although a model may be estimated using linear techniques, forecasts wi...

Objective. This study examines how racial/ethnic self-identity interrelates with language ability, skin tone, and years in the United States and with indicators of socioeconomic attainment for Dominican immigrants in Reading, Pennsylvania, a new destination city that had a nearly 800 percent increase in the Dominican population between 1990–2000. Methods. In-depth ethno-surveys conducted with a...

I’ll present some recent work with F. Planchon on bilinear virial identities for the nonlinear Schrodinger equation, which are extensions of the Morawetz interaction inequalities firstly obtained by Colliander, Keel, Staffilani, Takaoka and Tao. We recover and extend known bilinear improvements to Strichartz inequalities and provide applications to various nonlinear problems, most notably on do...

TheWard identities of the W∞ symmetry in two dimensional string theory in the tachyon background are studied in the continuum approach. We consider amplitudes different from 2D string ones by the external leg factor and derive the recursion relations among them. The recursion relations have non-linear terms which give relations among the amplitudes defined on different genus. The solutions agre...

We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual pr...

We study utility indifference pricing of claim streams with intertemporal consumption and power (CRRA) utilities. We derive explicit formulas for the derivatives of the utility indifference price with respect to claims and wealth. The simple structure of these formulas is a reflection of surprising operator identities for the derivatives of the optimal consumption stream. For example, the parti...

Using matrix identities, we construct explicit pseudo-exponential-type solutions of linear Dirac, Loewner and Schrödinger equations depending on two variables and of nonlinear wave equations depending on three variables.

In this paper, we consider a two-dimensional model for finite set partitions which arises in conjunction with a special case of a general non-linear recurrence. We investigate properties of some of the related counting sequences, including recurrences and generating functions. In particular, we obtain, by combinatorial arguments, some formulas relating these sequences to the Stirling numbers of...

The necessary and sufficient condition for the existence of αsurfaces in complex space-time manifolds with nonvanishing torsion is derived. For these manifolds, Lie brackets of vector fields and spinor Ricci identities contain explicitly the effects of torsion. This leads to an integrability condition for α-surfaces which does not involve just the self-dual Weyl spinor, as in complexified gener...