Abstract
Parametric surface waves in water or liquefiable layers are described by a wave-type equation. Approximate solutions of this equation are presented. These solutions describe unfamiliar waves which can have properties of both standing waves and travelling waves. They are a new kind of waves which are not d’Alembert-type waves. Analytic expressions for different periodical wave patterns in the x–t plane are found. Theoretical results are compared with recent experimental data. It is noted that the solutions may be valid for different wave fields of Nature. According to the theory an infinite quantity of localised modes may be generated in the fields due to any periodical parametric excitation. Sometimes these modes are indistinguishable from particles. Thus the equation which is also valid for springs and lattices has a rich variety of nonlinear solutions. This variety is huge in comparison with a variety of solutions of ordinary differential equations.
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