| Abstrakt: |
Conclusions In this short lecture we have expounded only a portion of the methods that have currently been developed for finding exact solutions of problems in the nonlinear theory of waves. They have been used for an exact solution of a large number of model equations, although, as has already been noted, the derivation of these equations is frequently approximate [3, 83]. Numerous publications are currently, as is evident from the bibliography, devoted mainly to proof of the applicability of various approaches to equations that have already been studied and to the application of a definite methodological generality. However, the number of equations of interest for application purposes that have been solved exactly is for the time being increasing slowly. It may be hoped that familiarity with new ideas in this field will lead to a noticeable increase in the number of solvable equations. The joint application of exact, approximate and numerical methods (which Zabusky has combined in the term “synenergetic” approach [84]) will allow a significant advance in the understanding of the general picture of wave processes in nonlinear dispersive media. |
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