Solitons in a One‐Dimensional Modified Hubbard Model

Abstract

It is shown, that in a Hubbard chain modified by coupling to the lattice solitons e x i s w h e y are accompanied by solitary lattice distortions. The non-linearity is caused by the electron correlation as well as by the electron-phonon interaction.Es wird gezeigt, daS in ciner Hubbardkette, die durch Kopplung an das Gitter modifiziert ist, Solitonen existieren, die von solitaren Gitterstorungen begleitet sind. Die Nichtlinearitiit wird sowohl durch die Elektronenkorrelation als auch durch die Elektron-Phonon-Wechselwirkung verarsacht.

Generating multibreather vector solitons by influencing the Manakov model and its modified forms with the linear self and cross coupling parameters

“…Further this BD vector soliton solution and other possible solutions of the modified equation with mixed nonlinearities obtained by simultaneously changing the signs of SPM and dispersion coefficients of any one of its scalar component can be directly derived through the simple transformations realized by comparing the Hirota bilinear forms of the Manakov model and its modified form as shown in the section 2 . Section 3 reveals that all such solutions modify their nature as multibreather vector one-solitons with different breathing maps, if the linear coupling terms are added suitably in the respective Manakov model and its modified form without loss of their integrability properties in accordance with many earlier studies [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] , [50] . Moreover the number of soliton and anti-soliton parts composed in each breather with a definite breathing length can be controlled by tuning its free parameters for pulse-width, velocity, and depth of localization appropriately.…”

“…In the modified Manakov case, one can directly realize the dark–dark [10] , the bright–bright [33] , [34] , and the bright–dark [35] , [36] , [37] vector soliton solutions by making trivial changes in the corresponding manipulations made for the Manakov case by using the Hirota's technique. The possible physical realizations of such modified Manakov model arise in the contexts of Boson–Fermion gas mixtures [38] , [39] , BECs involving two isotopes of the same element [40] , multi-field propagation in a quadratic medium with inefficient phase matching [41] and Bose–Hubbad model [42] . Moreover Lazarides and Tsironis [22] have used the Eq.…”

Two‐Soliton Solution in a Modified Hubbard Chain

“…I n time-dependent, mean-field approximation and in the continuum limit our model [2] is represented by the Lagrangian density [4] 178 U. LINDNER and S. SCHERF with the condition (a/aE) c @ : @ -@ = 0 a t the boundary of the system if we start from an antiferromagnetic'ground state order. % is the Hamilton density, x(5, t ) is the deviation of a lattice particle related to the lattice constant a from the equilibrium position, L D~ = KIM, where oc is the force constant and M denotes the mass of a lattice particle.…”

Solitons in a One-Dimensional Degenerate Hubbard Model

“…[1][2][3][4][5][6][7][8][9]). One of the possible sources of nonlinearity is the electron-phonon coupling.…”