Solitons and Compactons
Part of the Nonlinear Physical Science book series (NPS)
In 1834, John Scott Russell was the first to observe the solitary waves. He observed a large protrusion of water slowly traveling on the Edinburgh-Glasgow canal without change in shape. The bulge of water, that he observed and called “great wave of translation”, was traveling along the channel of water for a long period of time wile still retaining its shape. The remarkable discovery motivated Russell to conduct physical laboratory experiments to emphasize his observance and to study these solitary waves. He empirically derived the relation
$$ c^2 = g(h + a), $$
KeywordsSolitary Wave Boussinesq Equation Solitary Wave Solution Adomian Decomposition Method Exponential Tail
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