Equation for three-dimensional nonlinear waves in liquid with gas bubbles

Details Equation for three-dimensional nonlinear waves in liquid with gas bubbles Equation for three-dimensional nonlinear waves in liquid with gas bubbles

2012-01-22

arxiv.org/abs/1201.4583v1

2012 Phys. Scr. 85 025402

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1088/0031-8949/85/02/025402

Nonlinear waves in a liquid containing gas bubbles are considered in the three-dimensional case. Nonlinear evolution equation is given for description of long nonlinear pressure waves. It is shown that in the general case the equation is not integrable. Some exact solutions for the nonlinear evolution equation are presented. Application of the Hirota method is illustrated for finding multi-soliton solutions for the nonintegrable evolution equation in the three-dimensional case. The stability of the one-dimensional solitary waves is investigated. It is shown that the one-dimensional solitary waves are stable to transverse perturbations.

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