A.N.Serdjuchenko Evolution Schredinger equations of high orders and some their solutions for deep water surface waves |
Applied hydromechanics, Vol. 3 (75) ¹ 2, (2001) |
| Nonlinear Schredinger equations (NLS) of III to V-th orders for deep water surface wave groups, describing temporal and spatial evolution of complex amplitude of fundamental harmonic in velocity potential of wave motion are considered. NLS-equations have been systematically derived for the first five orders in the framework of the solution of nonlinear boundary value probrem for deep water wavesof finite amplitude by using multi scale technique. Nonlinearity, irregularity and 3D effects of wave motion and surface wind pressure action ware included into the consideration. Different combinations of independent slowly varying variables (scales) and corresponding versions of NLS-equations have been considered and discussed. In addition to NLS-equations, linear equations for complex amplitude in fluid domain and linear boundary value problems for drift velocity potential, induced by amplitude modulation of wave motion and associated with NLS-equations, ware considered too. Permanent solutions including not only wall-known solitary and periodical solutions but some new solutions in elliptic Vejerstrass functions have been derived. |
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| TEXT LANGUAGE: Russian |