Lump solitons in a higher-order nonlinear equation in 2+1 dimensions

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrodinger equation to 2 + 1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Rational choice, social identity, and beliefs about oneself

Social identity poses one of the most important challenges to rational choice theory, but rational choice theorists do not hold a common position regarding identity. On one hand, externalist rational choice ignores the concept of identity or reduces it to revealed preferences. On the other hand, internalist rational choice considers identity as a key concept in explaining social action because it permits expressive motivations to be included in the models. However, internalist theorists tend to reduce identity to desire—the desire of a person to express his or her social being. From an internalist point of view, that is, from a viewpoint in which not only desires but also beliefs play a key role in social explanations as mental entities, this article rejects externalist reductionism and proposes a redefinition of social identity as a net of beliefs about oneself, beliefs that are indexical, robust, and socially shaped.