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Compact and noncompact structures for a variant of KdV equation in higher dimensions. (English) Zbl 1031.35128
Summary: We study two mathematical variants of the KdV equation. We show that the focusing branches of these variants exhibit compactons: solitons with finite wavelength, whereas the defocusing branches support solitary patterns solutions with cusps or infinite slopes. A framework is developed for studying these problems in higher dimensions. Two distinct sets of general formulas for each type of variants are developed to present a fairly complete understanding of the compact and noncompact dispersive structures.

35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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