In this Letter, we analyze the structure of linearization operators of the Korteweg–de Vries (KdV) hierarchy equations expanded around single-soliton solutions. We uncover the remarkable property that these linearization operators can be factored into the integro-differential operator which generates this hierarchy and the linearization operator of the KdV equation. An important consequence of ...

De ne a C* algebra A over the quaternions H as follows: First, A should be an algebra in the usual sense over the reals R, and A should be a left and right vector space over H, where the di erent senses of scalar multiplication by a real agree. Then extend associativity by h(ab) = (ha)b, (ah)b = a(hb), (ab)h = a(bh), and (ha)i = h(ai), where (as always here) a, b ∈ A and h, i ∈ H. Let ∗ be an i...

K.M. Lynch,1 J. Billowes,1 I. Budincevic,2 T.E. Cocolios,1 R.P. De Groote,2 S. De Schepper,2 K.T. Flanagan,1 R.F. Garcia Ruiz,2 H. Heylen,2 B.A. Marsh,3 G. Neyens,2 T.J. Procter,1 S. Rothe,4 G.S. Simpson,5 A.J. Smith,1 H.H. Stroke,6 and K. Wendt4 1School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, United Kingdom 2Instituut voor Kernen Stralingsfysica, KU Leuven,...

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial diffe...

The Dushnik-Miller dimension of a poset ≤ is the minimal number d of linear extensions ≤1, . . . ,≤d of ≤ such that ≤ is the intersection of ≤1, . . . ,≤d. Supremum sections are simplicial complexes introduced by Scarf [13] and are linked to the Dushnik-Miller as follows: the inclusion poset of a simplicial complex is of Dushnik-Miller dimension at most d if and only if it is included in a supr...

Luis Ulisses Signori, Alexandre Schaan de Quadros, Graciele Sbruzzi, Thiago Dipp, Renato D. Lopes, Beatriz D’Agord Schaan I Universidade Federal do Rio Grande, Instituto de Ciências Biológicas, Rio Grande/RS, Brazil. II Instituto de Cardiologia do Rio Grande do Sul/Fundação Universitária de Cardiologia, Porto Alegre/RS, Brazil. III Duke University Medical Center, Duke Clinical Research Institut...

The initial boundary-value problem for the Korteweg–de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual initial boundary-value problem on the positive quarter-plane, for which x > 0 and t > 0. Two boundary conditions are required at x = 0 for the negative quarter-plane problem, in contrast to the one bo...

The Korteweg-de Vries (KdV) equation is known as a model of long waves in an infinitely long canal over a flat bottom and approximates the two-dimensional water wave problem, which is a free boundary problem for incompressible Euler equation with the irrotational condition. In this paper, we consider the validity of this approximation in the case of presence of surface tension. Moreover, we con...

Vanessa de Fátima Bernardes; Luis Otávio de Miranda Cota; Fernando de Oliveira Costa; Ricardo Alves Mesquita; Ricardo Santiago Gomez; Maria Cássia Ferreira Aguiar DDS, MS, Graduate student, Department of Oral Surgery and Pathology, School of Dentistry, Federal University of Minas Gerais, Brazil DDS, MS, PhD, Adjunct Professor, Department of Oral Surgery and Pathology, School of Dentistry, Feder...