On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

L1CAM binds ErbB receptors through Ig-like domains coupling cell adhesion and neuregulin signalling.

During nervous system development different cell-to-cell communication mechanisms operate in parallel guiding migrating neurons and growing axons to generate complex arrays of neural circuits. How such a system works in coordination is not well understood. Cross-regulatory interactions between different signalling pathways and redundancy between them can increase precision and fidelity of guidance systems. Immunoglobulin superfamily proteins of the NCAM and L1 families couple specific substrate recognition and cell adhesion with the activation of receptor tyrosine kinases. Thus it has been shown that L1CAM-mediated cell adhesion promotes the activation of the EGFR (erbB1) from Drosophila to humans. Here we explore the specificity of the molecular interaction between L1CAM and the erbB receptor family. We show that L1CAM binds physically erbB receptors in both heterologous systems and the mammalian developing brain. Different Ig-like domains located in the extracellular part of L1CAM can support this interaction. Interestingly, binding of L1CAM to erbB enhances its response to neuregulins. During development this may synergize with the activation of erbB receptors through L1CAM homophilic interactions, conferring diffusible neuregulins specificity for cells or axons that interact with the substrate through L1CAM

Towards a theory of differential constraints of a hydrodynamic hierarchy

We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative examples and new integrable models are exhibited.Comment: Published by JNMP at http://www.sm.luth.se/math/JNMP

`Interpolating' differential reductions of multidimensional integrable hierarchies

We transfer the scheme of constructing differential reductions, developed recently for the case of the Manakov-Santini hierarchy, to the general multidimensional case. We consider in more detail the four-dimensional case, connected with the second heavenly equation and its generalization proposed by Dunajski. We give a characterization of differential reductions in terms of the Lax-Sato equations as well as in the framework of the dressing method based on nonlinear Riemann-Hilbert problem.Comment: Based on the talk at NLPVI, Gallipoli, 15 page

VP64.21: Endometrial thickness, ovarian dimensions and oocyte count in women following bariatric surgery and exercise: preliminary findings from the EMOVAR RCT

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