摘要:

Givenp∈ N = {1, 2, 3 ...}, as a generalization of the 3x+ 1 problem [7], we study the behavior of the sequencess(m) = {mn}n ≥ 0,m∈ Z (the set of the integers), defined by the iterative formulaandar=tr/p(tr∈ N), andbrare chosen in such a way thatmn∈ Z for everyn. Our aim is to establish when these sequences are divergent, or convergent into a cycle, considering also a fixed point as a cycle. Moreover, the structure of possible cycles is inv

ISSN:0022-2526    

DOI:10.1002/sapm1992863185

年代:1992

数据来源: WILEY

摘要:

The 2 + 1‐modified Kadomtsev‐Petviashvili (mKP) equation is studied by the inverse‐spectral‐transform method. The initial‐value problems for the mKP‐1 and mKP‐11 equations are solved by the nonlocal Riemann‐Hilbert and techniques for initial data decaying sufficiently rapidly at infinity. The lump solutions for the mKP‐I equation are found explicitly. Wide classes of the exact solutions for the mKP equation—namely, the rational solutions, including the plane lumps for the mKP‐I equation; solutions with functional parameters; the plane solitons; and breathers—are constructed by the use of themethod based on the nonlocal . The Miura transformation between the mKP and KP

ISSN:0022-2526    

DOI:10.1002/sapm1992863219

年代:1992

数据来源: WILEY