Nonlinear Waves in the Magnetically Structured Solar Atmosphere

Response to “Comment on ‘Slow nonlinear waves in magnetic flux tubes'” [Phys. Plasmas 12, 034701 (2005)]

“…I meant in this case the discussion of Ruderman 6 whether there is slow surface solitons for any amplitudes. As explained above, the discussion of this kind is nothing else as the discussion of nonlinear wave properties, which are defined by the dispersion behavior beyond the long-wave approximation.…”

“…The author of the Comment makes many efforts 1,6 to show that the KdV equation for slow body waves, derived by Zhugzhda and Nakariakov, 8,9 is not correct and has to be putted an outlaw. I agree with Ruderman that the dispersion law used to obtain this equation is asymptotically incorrect, since the only dispersion defined by the second term in Eq.…”

“…͑The surface solitary waves appear as a bulge of the tube.͒ The Zhugzhda and Nakariakov equation puts an end to long standing confusion due to the Molotovshikov and Ruderman paper 4 that dispersive nonlinear body waves do not exist. This confusion appeared due to the Khochlov-Zabolotskaya equation 4,6 which, as explained above, is valid only for the body waves in isolated flux tubes. Besides, the effect of the pressure catastrophe in the throat of the tube contraction produced by body wave was revealed also due to the Zhugzhda and Nakariakov equation.…”

“…Ruderman is responsible for the mess in the theory of slow waves in flux tubes since he mixed surface and body waves 6 and claimed that his KhochlovZabolotskaya equation is valid for body waves affected by external plasma. He calls these crucial mistakes as a methodological ones and would not like to admit them.…”

“…Ruderman's proposal to introduce a new term "pseudobody slow wave" leads to the new mess instead of the earlier confusion. 4,6 …”