Titov А V. RussiaSaratov Saratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, Russia Titovav88@gmail.com Additional info Аспирант СГУ. Author's articles AN APPROXIMATE NONLINEAR THEORY OF DOUBLE-STREAM INSTABILITY DISPERSION EQUATION FOR VARIOUS MODELS OF PIERCE DIODE TWO-STREAM INSTABILITY – LINEAR AND NONLINEAR MICROWAVE PHENOMENA TWO-STREAM INSTABILITY – LINEAR AND NONLINEAR MICROWAVE PHENOMENA