α Corresponding author: [email protected] These authors contributed equally to this work. Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany Institute for Nonlinear Dynamics, Georg-August-Universität, Göttingen, Germany German Center for Cardiovascular Research (DZHK), partner site Göttingen, Germany Institute of Pharmacology and Toxicology, University Medical Cen...

We study the self-similar solutions for nonlinear Schrödinger type equations of higher order with nonlinear term |u|u by a scaling technique and the contractive mapping method. For some admissible value α, we establish the global well-posedness of the Cauchy problem for nonlinear Schrödinger equations of higher order in some nonstandard function spaces which contain many homogeneous functions. ...

By using the quantum hydrodynamic and Maxwell equations, we derive the generalized nonlinear electron magnetohydrodynamic, the generalized nonlinear Hall-MHD HMHD , and the generalized nonlinear dust HMHD equations in a self-gravitating dense magnetoplasma. Our nonlinear equations include the self-gravitating, the electromagnetic, the quantum statistical electron pressure, as well as the quantu...

Nonlinear acoustic processes of second harmonic generation and nonlinear resonances in a diatomic granular chain (a granular phononic crystal) with static precompression are reported. The observed nonlinear self-action process which manifests itself as shifts in resonance frequencies of the chain leads to amplitude-dependent band edges: the properties of the phononic crystal change as a functio...

we consider a new type of integrable coupled nonlinear schrodinger (cnls)equations proposed by our self [submitted to phys. plasmas (2011)]. the explicitform of soliton solutions are derived using the hirota's bilinear method.we show that the parameters in the cnls equations only determine the regionsfor the existence of bright and dark soliton solutions. finally, throughthe linear stabili...