Grassmannian flows and applications to nonlinear partial differential equations

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto a coordinate chart of the underlying Grassmann manifold. Our method relies on extending this idea to the infinite dimensional case. The key is an integral equation analogous to the Marchenko equation in integrable systems, that represents the coodinate chart map. We show explicitly how to generate such solutions to scalar partial differential equations of arbitrary order with nonlocal quadratic nonlinearities using our approach. We provide numerical simulations that demonstrate the generation of solutions to Fisher--Kolmogorov--Petrovskii--Piskunov equations with nonlocal nonlinearities. We also indicate how the method might extend to more general classes of nonlinear partial differential systems.Comment: 26 pages, 2 figure

Gender and sustainable livelihoods: linking gendered experiences of environment, community and self

In this essay I explore the economic, social, environmental and cultural changes taking place in Bolsena, Italy, where agricultural livelihoods have rapidly diminished in the last two decades. I examine how gender dynamics have shifted with the changing values and livelihoods of Bolsena through three women’s narratives detailing their gendered experiences of environment, community and self. I reflect on these changes with Sabrina, who is engaged in a feminist community-based organization; Anna, who is running an alternative wine bar; and Isabella, a jeweler, who is engaged in ecofeminist practices. My analysis is based on concepts developed by feminist political ecology: specifically, the theory of rooted networks from Dianne Rocheleau, Donna Haraway’s concept of naturecultures (and the work of J. K. Gibson-Graham on new economic imaginaries emerging from the politics of place. I aim to think with, reflect upon and provoke from the ‘‘otherwise’’, taking into account the lived relations entwining nature and gender. My article looks at the interconnections of gender, environment and livelihoods, attentive to the daily needs, embodied interactions and labours of these three women as part of a reappropriation, reconstruction and reinvention of Bolsena’s lifeworld. By listening to the stories of their everyday lives and struggles, I show the dynamic potential of the politics of place and the efforts to build diverse economies and more ethical economic and ecological relationships based on gender-aware subjectivities and values

The Fredholm determinant method for discrete integrable evolution equations

TIB: RN 7349 (371) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman