| Nonlinear stationary waves and solitary waves in fluid systems with long-range forces (1993) | |||||||||||||
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| PhysicsLettersA North Holland PHYSICS LETTERS Nonlinear stationary waves and solitary waves fluid systems with long range forces Fred Adams Marco Fatuzzo and Richard Watkins Physics Department University ofMichigan Ann Arbor USA Received June accepted forpublication September Communicated Holm study class nonlinear model equations which represent one dimensional fluid systems with long range forces such gravity present elementary theorems which constrain the allowed types stationary wave and solitary wave solutions for this class systems Introduction wide variety nonlinear wave structures can exist fluid systems where self gravity important but such motions have not been well studied These waves are most likely occur astrophysical settings although many other physical systems with long range forces can mathematically resemble this problem see below this Letter consider class nonlinear equations which model self gravitating fluid systems one spatial dimension Our goal find general results which show how physical properties such systems determine the allowed types stationary wave solutions Fluid motions which simultaneously include both self gravity and nonlinear effects can exhibit interesting behavior general most nonlinear waves fluids tend steepen and shock the other hand self gravity leads dispersion which tends spread out wave packets principle fluids with self gravity can reach balance between nonlinear steepening and gravitational dispersion This balance leads the possi. Peer Reviewed. http://deepblue.lib.umich.edu/bitstream/2027.42/30449/1/0000073.pdf | |||||||||||||
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