2013/01/29 by O. M. Kiselev, Kiselev, O. M.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS) #math-ph #math.MP #nlin.PS
paper · pdf · doi:10.48550/arxiv.1301.6885
8 pages in Russian
arxiv created 2013/01/29 · arxiv updated 2013/01/30
The primary resonance equation in partial derivatives with external force and slowly varying frequency is derived. The leading-order term of asymptotic solution is constructed as a soliton with growing amplitude when time is large. This growing solution is obtained due to the decaying amplitude of the external force. A necessary condition for the growth of the solution in dissipative media is obtained also.