Soliton molecules have been experimentally discovered in optics and theoretically investigated for coupled systems. This paper is concerned with the formation of soliton molecules by the resonant mechanism for a noncoupled system, the Sharma-Tasso-Olver-Burgers (STOB) equation. In terms of introducing velocity resonance conditions, we derive the soliton (kink) molecules, half periodic kink (HPK) molecules and breathing soliton molecule of STOB equation. Meanwhile, the fission and fusion phenomena among kinks, kink molecules, HPKs and HPK molecules have been revealed. Moreover, we also discuss the central periodic kink solutions from the multiple solitary wave solutions.Solitons have been experimentally found in plasma physics and optics, as well as in nonlinear science area including Bose-Einstein condensation and DNA mechanical waves [15,16]. It is wellknown that solitons have an important application in a variety of areas, such as atmospheric and ocean dynamics [17], optical fibers [18]-[22], photonic crystals [23] and plasmas [24]. Later on the soliton molecules which are the soliton bound states have attracted considerable attention. Soliton molecules have been observed in optical systems [25]-[29] and analyzed in Bose-Einstein condensates [30]. Various theoretical proposals to form soliton molecules have been established [31]-[33]. It is known that soliton molecules in coupled systems have been well discussed [34]. Recently, the breathing soliton molecules have been experimentally observed in a mode-locked fiber laser [28]. The resonant theory of solitons is applicable to a variety of integrable systems, such as the KP-(II) equation [35, 36] and Novikov-Veselov equation [37] in which Wronskian representation of the τ -function have been employed. By restricting different resonant conditions on the solitons, it may derive many types resonant excitations. The resonant solutions have been generated by using linear superposition principle and the Bell polynomials for the bilinear equations [38]. By virtue of Hirotas direct method and the Bäcklund transformation, the researchers study the fission and fusion of the solitary wave solution of the Burgers and STO equations [14]. Furthermore, the interaction between the lump soliton and the pair of resonance stripe solitons form a rogue wave solution [39]. The rational solutions to the modified Korteweg-de Vries equation have been analyzed by imposing the wave number resonance constraints [40]. Lately, by means of introducing velocity resonant mechanism, Lou investigated some types of soliton molecules in fluid systems [41] and nonlinear optical systems [42] involving the third-fifth order Korteweg de-Vries (KdV) equation, the KdV-Sawada-Kotera (KdVSK) equation, the KdV-Kaup-Kupershmidt (KdVKK) equation, the Hirota system and the potential modified KdV-sG system which derive kink-kink molecule, kink-antikink molecule, kink-breather molecule and breatherbreather molecule etc. Although the structure and properties of the integrable systems have been widely investigated,...

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The q-deformation of the infinite-dimensional n-algebra is investigated. Based on the structure of the q-deformed Virasoro-Witt algebra, we derive a nontrivial q-deformed Virasoro-Witt n-algebra which is nothing but a sh-n-Lie algebra. Furthermore in terms of the pseuddifferential operators on the quantum plane, we construct the (co)sine n-algebra and the q-deformed SDif f (T 2 ) n-algebra. We prove that they are the sh-n-Lie algebras for the case of even n. An explicit physical realization of the (co)sine n-algebra is given.

The Heisenberg supermagnet model is an integrable supersymmetric system and has a close relationship with the strong electron correlated Hubbard model. In this paper, we investigate the integrable higher order deformations of Heisenberg supermagnet models with two different constraints: (i) S2=3S−2I for S∊USPL(2/1)/S(U(2)×U(1)) and (ii) S2=S for S∊USPL(2/1)/S(L(1/1)×U(1)). In terms of the gauge transformation, their corresponding gauge equivalent counterparts are derived.

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