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Compactons and solitary patterns structures for variants of the KdV and the KP equations. (English) Zbl 1029.35200
Summary: We discuss mathematical variants in higher dimensions of the KdV and the KP equations. It is shown that the focusing branches of these variants exhibit compactons: solitons with finite wavelength, whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps. The study presents a fairly complete understanding of the compact and noncompact dispersive structures.

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